# Load required packages
pacman::p_load(httr, jsonlite)
# Url of datamall
url <- "https://datamall2.mytransport.sg/ltaodataservice/PV/ODBus"
# Update query params and header
query_params <- list(Date = "202409") # Replace date as required
headers <- httr::add_headers(
AccountKey = "Replace_with_AccountKey"
)
# Make the GET request
response <- httr::GET(url, query = query_params, headers)Hands-On Exercise 10
Data Sources
(saved under ‘data’ folder)
| Data | Source | Description |
|---|---|---|
| BusStop | LTA DataMall | A point representation to indicate the position where buses should stop to pick up or drop off passengers. |
| MPSZ-2019 | data.gov.sg | Sub-zone boundary of URA Master Plan 2019 |
| origin_destination_bus_202409 | LTA DataMall | Passenger volume by origin destination bus stops |
The passenger volume by origin destination bus stops is slightly more tricky to obtain given that it is a dynamic dataset. Users are required to go through the following:
- Request for API access at LTA DataMall
- LTA DataMall will send an email with the user’s API Account Key
- Now, I can simply use packages such as
httrandjsonliteto make an API request - The url from the response will be used to download the data, unzipped into the relevant folder.
# Parse the response if it's in JSON
if (status_code(response) == 200) {
content <- content(response, "text")
json_data <- fromJSON(content)
# Assuming the response contains a field 'zip_url' with the file URL
zip_url <- json_data$value$Link
# Download the ZIP file
download.file(zip_url, destfile = "data.zip", mode = "wb")
# Unzip the file to a directory
unzip("data.zip", exdir = "data/aspatial")
# Optionally, list the contents of the unzipped directory
list.files("unzipped_data")
# Delete the ZIP file after unzipping
unlink("data.zip")
}Chapter 15: Processing and Visualising Flow Data
15.1 Setting Up
Spatial interaction represent the flow of people, material, or information between locations in geographical space. It encompasses everything from freight shipments, energy flows, and the global trade in rare antiquities, to flight schedules, rush hour woes, and pedestrian foot traffic.
Each spatial interaction, as an analogy for a set of movements, is composed of a discrete origin/destination pair. Each pair can be represented as a cell in a matrix where rows are related to the locations (centroids) of origin, while columns are related to locations (centroids) of destination. Such a matrix is commonly known as an origin/destination matrix, or a spatial interaction matrix.
The goal of this exercise is to:
- to import and extract OD data for a selected time interval,
- to import and save geospatial data (i.e. bus stops and mpsz) into sf tibble data frame objects,
- to populate planning subzone code into bus stops sf tibble data frame,
- to construct desire lines geospatial data from the OD data, and
- to visualise passenger volume by origin and destination bus stops by using the desire lines data.
15.1.1 Loading the R packages
-sf package to perform geospatial wrangling tasks
-sp package to calculate spatial distance
- DT package to visualize results in well-formatted tables
- tmap package for plotting tasks
- performance package for model metrics comparison
- ggpubr package for custom ggplots
-tidyverse and reshape2 package for reading csv files, dataframe processing tasks
pacman::p_load(tmap, sf, sp, DT, stplanr, tidyverse, reshape2, performance, ggpubr)15.1.2 Importing Aspatial Data
First, I will import the passenger volume by origin destination bus stops dataset which was downloaded via the API call. Then i’ll use glimpse() to check it.
# Load OD dataset
odbus <- read_csv("data/aspatial/origin_destination_bus_202409.csv")Rows: 5721503 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (5): YEAR_MONTH, DAY_TYPE, PT_TYPE, ORIGIN_PT_CODE, DESTINATION_PT_CODE
dbl (2): TIME_PER_HOUR, TOTAL_TRIPS
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# Check dataset
glimpse(odbus)Rows: 5,721,503
Columns: 7
$ YEAR_MONTH <chr> "2024-09", "2024-09", "2024-09", "2024-09", "2024-…
$ DAY_TYPE <chr> "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/…
$ TIME_PER_HOUR <dbl> 20, 19, 23, 14, 14, 18, 9, 15, 7, 21, 7, 7, 8, 10,…
$ PT_TYPE <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE <chr> "46009", "59091", "54181", "61039", "44629", "7720…
$ DESTINATION_PT_CODE <chr> "46249", "59419", "54201", "61111", "44009", "6441…
$ TOTAL_TRIPS <dbl> 586, 54, 72, 256, 902, 6, 5, 15, 6, 4, 76, 36, 3, …Since “ORIGIN_PT_CODE” and “DESTINATION_PT_CODE” is in string data type, I would need to convert them into factor data type.
# Convert to factor data type
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 15.1.3 Aspatial Data Wrangling
The study data is focused on weekdays between 6-9 o’clock. Therefore, the dataset needs to be filtered accordingly.
# Filter odbus
odbus6_9 <- odbus %>%
filter(DAY_TYPE == "WEEKDAY") %>%
filter(TIME_PER_HOUR >= 6 &
TIME_PER_HOUR <= 9) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))`summarise()` has grouped output by 'ORIGIN_PT_CODE'. You can override using
the `.groups` argument.datatable() from DT package will be used to display the filtered dataset.
# Use datatable to show filtered data
datatable(odbus6_9)Warning in instance$preRenderHook(instance): It seems your data is too big for
client-side DataTables. You may consider server-side processing:
https://rstudio.github.io/DT/server.htmlI will save this in rds for easy retrieval.
# Save to rds
write_rds(odbus6_9, "data/processed/odbus6_9.rds")This can also loaded back into R easiler
# Load odbus rds
odbus6_9 <- read_rds("data/processed/odbus6_9.rds")15.1.4 Importing Geospatial Data
Using st_read() from sf package, I will load in to geospatial datasets - busstop and mpsz. I will also do projection for both with st_transform() .
# Load bus stop dataset
busstop <- st_read(dsn = "data/geospatial",
layer = "BusStop") %>%
st_transform(crs = 3414)Reading layer `BusStop' from data source
`C:\Users\Henry\Desktop\SMU Masters\2024-2025 T1\Geospatial Analytics & Applications\Project\GeospatialWebsite\Hands-On_Ex\Hands-On_Ex_10\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 5166 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3970.122 ymin: 26482.1 xmax: 48285.52 ymax: 52983.82
Projected CRS: SVY21# Load mpsz dataset
mpsz <- st_read(dsn = "data/geospatial",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source
`C:\Users\Henry\Desktop\SMU Masters\2024-2025 T1\Geospatial Analytics & Applications\Project\GeospatialWebsite\Hands-On_Ex\Hands-On_Ex_10\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 84Now i will check the mpsz sf dataframe.
# Check mpsz
mpszSimple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
SUBZONE_N SUBZONE_C PLN_AREA_N PLN_AREA_C REGION_N
1 MARINA EAST MESZ01 MARINA EAST ME CENTRAL REGION
2 INSTITUTION HILL RVSZ05 RIVER VALLEY RV CENTRAL REGION
3 ROBERTSON QUAY SRSZ01 SINGAPORE RIVER SR CENTRAL REGION
4 JURONG ISLAND AND BUKOM WISZ01 WESTERN ISLANDS WI WEST REGION
5 FORT CANNING MUSZ02 MUSEUM MU CENTRAL REGION
6 MARINA EAST (MP) MPSZ05 MARINE PARADE MP CENTRAL REGION
7 SUDONG WISZ03 WESTERN ISLANDS WI WEST REGION
8 SEMAKAU WISZ02 WESTERN ISLANDS WI WEST REGION
9 SOUTHERN GROUP SISZ02 SOUTHERN ISLANDS SI CENTRAL REGION
10 SENTOSA SISZ01 SOUTHERN ISLANDS SI CENTRAL REGION
REGION_C geometry
1 CR MULTIPOLYGON (((33222.98 29...
2 CR MULTIPOLYGON (((28481.45 30...
3 CR MULTIPOLYGON (((28087.34 30...
4 WR MULTIPOLYGON (((14557.7 304...
5 CR MULTIPOLYGON (((29542.53 31...
6 CR MULTIPOLYGON (((35279.55 30...
7 WR MULTIPOLYGON (((15772.59 21...
8 WR MULTIPOLYGON (((19843.41 21...
9 CR MULTIPOLYGON (((30870.53 22...
10 CR MULTIPOLYGON (((26879.04 26...This will be saved to rds format for easy retrieval.
# Save to rds format
mpsz <- write_rds(mpsz, "data/processed/mpsz.rds")15.1.5 Geospatial Data Wrangling
First, I will combine the busstop sf dataframe with the mpsz sf dataframe with st_intersection() from sf package. Next, only the relevant fields are selected. Finally, st_drop_geometry() will be used to remove the geometry column.
# Combine and process busstop_mpsz dataframe
busstop_mpsz <- st_intersection(busstop, mpsz) %>%
select(BUS_STOP_N, SUBZONE_C) %>%
st_drop_geometry()Warning: attribute variables are assumed to be spatially constant throughout
all geometriesnrow(busstop) - nrow(busstop_mpsz)[1] 5
Note
5 bus stops are excluded in the result as they are outside of Singapore boundary
datatable() from DT package is used to show the data
# Check result
datatable(busstop_mpsz)I will save this as rds format for easy retrieval.
write_rds(busstop_mpsz, "data/processed/busstop_mpsz.rds") The planning subzone from busstop_mpsz dataframe can be appended to odbus6_9 with left_join(). The columns will also be renamed for consistency.
# Left join busstop_mpsz to odbus6_9 for origin pt code
od_data <- left_join(odbus6_9 , busstop_mpsz,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_SZ = SUBZONE_C,
DESTIN_BS = DESTINATION_PT_CODE)Warning in left_join(odbus6_9, busstop_mpsz, by = c(ORIGIN_PT_CODE = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 16245 of `x` matches multiple rows in `y`.
ℹ Row 674 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.
Note
Check for duplicates when doing left_join()
# Check for duplicates
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()Since there are duplicates, I need to retain the unique records.
# Get unique
od_data <- unique(od_data)The earlier code chunk can be rerun to check that there are no further duplicates. Next, I will update the od_data with planning subzone codes for the destination bus stops.
# Left join busstop_mpsz to odbus6_9 for destination pt code
od_data <- left_join(od_data , busstop_mpsz,
by = c("DESTIN_BS" = "BUS_STOP_N")) Warning in left_join(od_data, busstop_mpsz, by = c(DESTIN_BS = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 162 of `x` matches multiple rows in `y`.
ℹ Row 673 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.Again, I need to check for duplicates.
# Check for duplicates
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()Since there are duplicates, I will need to use unique() again.
# Get unique data
od_data <- unique(od_data)Finally, I will do some minor processing tasks
- Rename column
- Remove na
- Summarise number of trips by ORIGIN_SZ and DESTIN_SZ
# Process od_data
od_data <- od_data %>%
rename(DESTIN_SZ = SUBZONE_C) %>%
drop_na() %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarise(MORNING_PEAK = sum(TRIPS))`summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.With this, I can save the output into rds.
# Save to rds
write_rds(od_data, "data/processed/od_data_fii.rds")
# Read from rds
od_data_fii <- read_rds("data/processed/od_data_fii.rds")15.2 Visualizing Spatial Interaction
15.2.1 Create Desire Line
Using stplanr package, I will prepare a desire line.
First, i need to remove intra-zonal flows. The output will be saved in rds.
# Remove intra-zonal flows
od_data_fij <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]
# Save output to rds
write_rds(od_data_fij, "data/processed/od_data_fij.rds")
# Read from rds
od_data_fij <- read_rds("data/processed/od_data_fij.rds")od2line() from stplanr package will then be used to create the desire lines. This will also be saved into rds
# Create desire line
flowLine <- od2line(flow = od_data_fij,
zones = mpsz,
zone_code = "SUBZONE_C")Creating centroids representing desire line start and end points.# Save output to rds
write_rds(flowLine, "data/processed/flowLine.rds")
# Read from rds
flowLine <- read_rds("data/processed/flowLine.rds")15.2.2 Visualize Desire Lines
tmap package will be used to visualize the desire lines.
# Visualize desire lines
tm_shape(mpsz) +
tm_polygons() +
flowLine %>%
tm_shape() +
tm_lines(lwd = "MORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.3)Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object length
Since the flow data is very messy, I should focus on selected flows (i.e. those greater than or equal to 5000).
# Updated visualization of desire lines
tm_shape(mpsz) +
tm_polygons() +
flowLine %>%
filter(MORNING_PEAK >= 5000) %>%
tm_shape() +
tm_lines(lwd = "MORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6,
alpha = 0.3)Warning in g$scale * (w_legend/maxW): longer object length is not a multiple of
shorter object lengthWarning in g$scale * (x/maxW): longer object length is not a multiple of
shorter object length
Chapter 16: Calibrating Spatial Interaction Models with R
16.1 Setting Up
Spatial Interaction Models (SIMs) are mathematical models for estimating flows between spatial entities developed by Alan Wilson in the late 1960s and early 1970, with considerable uptake and refinement for transport modelling since then Boyce and Williams (2015).
Note
There are four main types of traditional SIMs (Wilson 1971):
- Unconstrained
- Production-constrained
- Attraction-constrained
- Doubly-constrained
The objective of this section is to calibrate SIM to determine factors affecting the public bus passenger flows during the morning peak in Singapore
16.2 Compute Distance Matrix
First, I’ll load in the mpsz sf dataframe again.
# Load mpsz
mpsz <- read_rds("data/processed/mpsz.rds")
# Check sf dataframe
mpszSimple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21 / Singapore TM
First 10 features:
SUBZONE_N SUBZONE_C PLN_AREA_N PLN_AREA_C REGION_N
1 MARINA EAST MESZ01 MARINA EAST ME CENTRAL REGION
2 INSTITUTION HILL RVSZ05 RIVER VALLEY RV CENTRAL REGION
3 ROBERTSON QUAY SRSZ01 SINGAPORE RIVER SR CENTRAL REGION
4 JURONG ISLAND AND BUKOM WISZ01 WESTERN ISLANDS WI WEST REGION
5 FORT CANNING MUSZ02 MUSEUM MU CENTRAL REGION
6 MARINA EAST (MP) MPSZ05 MARINE PARADE MP CENTRAL REGION
7 SUDONG WISZ03 WESTERN ISLANDS WI WEST REGION
8 SEMAKAU WISZ02 WESTERN ISLANDS WI WEST REGION
9 SOUTHERN GROUP SISZ02 SOUTHERN ISLANDS SI CENTRAL REGION
10 SENTOSA SISZ01 SOUTHERN ISLANDS SI CENTRAL REGION
REGION_C geometry
1 CR MULTIPOLYGON (((33222.98 29...
2 CR MULTIPOLYGON (((28481.45 30...
3 CR MULTIPOLYGON (((28087.34 30...
4 WR MULTIPOLYGON (((14557.7 304...
5 CR MULTIPOLYGON (((29542.53 31...
6 CR MULTIPOLYGON (((35279.55 30...
7 WR MULTIPOLYGON (((15772.59 21...
8 WR MULTIPOLYGON (((19843.41 21...
9 CR MULTIPOLYGON (((30870.53 22...
10 CR MULTIPOLYGON (((26879.04 26...To compute the distance matrix, I need to first convert the sf dataframe into a SpatialPolygonsDataFrame with as.Spatial().
# Convert into spatialpolygonsdataframe
mpsz_sp <- as_Spatial(mpsz)
# Check output
mpsz_spclass : SpatialPolygonsDataFrame
features : 332
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 6
names : SUBZONE_N, SUBZONE_C, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C
min values : ADMIRALTY, AMSZ01, ANG MO KIO, AM, CENTRAL REGION, CR
max values : YUNNAN, YSSZ09, YISHUN, YS, WEST REGION, WR Now, i can compute the distance matrix with spDists()
# Compute distance matrix
dist <- spDists(mpsz_sp,
longlat = FALSE)
# Check distance matrix
head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.000 3926.0025 3939.108 20252.964 2989.9839 1431.330 19211.836
[2,] 3926.003 0.0000 305.737 16513.865 951.8314 5254.066 16242.523
[3,] 3939.108 305.7370 0.000 16412.062 1045.9088 5299.849 16026.146
[4,] 20252.964 16513.8648 16412.062 0.000 17450.3044 21665.795 7229.017
[5,] 2989.984 951.8314 1045.909 17450.304 0.0000 4303.232 17020.916
[6,] 1431.330 5254.0664 5299.849 21665.795 4303.2323 0.000 20617.082
[7,] 19211.836 16242.5230 16026.146 7229.017 17020.9161 20617.082 0.000
[8,] 14960.942 12749.4101 12477.871 11284.279 13336.0421 16281.453 5606.082
[9,] 7515.256 7934.8082 7649.776 18427.503 7801.6163 8403.896 14810.930
[10,] 6391.342 4975.0021 4669.295 15469.566 5226.8731 7707.091 13111.391
[,8] [,9] [,10]
[1,] 14960.942 7515.256 6391.342
[2,] 12749.410 7934.808 4975.002
[3,] 12477.871 7649.776 4669.295
[4,] 11284.279 18427.503 15469.566
[5,] 13336.042 7801.616 5226.873
[6,] 16281.453 8403.896 7707.091
[7,] 5606.082 14810.930 13111.391
[8,] 0.000 9472.024 8575.490
[9,] 9472.024 0.000 3780.800
[10,] 8575.490 3780.800 0.000Additional processing steps are be done:
- Label column and row headers
- Pivot from wide to long format
- Update intra-zonal distances
- Rename origin and destination fields
# Prepare subzone codes
sz_names <- mpsz$SUBZONE_C
# Attach subzone codes to row and column
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)# Pivot from wide to long
distPair <- melt(dist) %>%
rename(dist = value)
# Check output
head(distPair, 10) Var1 Var2 dist
1 MESZ01 MESZ01 0.000
2 RVSZ05 MESZ01 3926.003
3 SRSZ01 MESZ01 3939.108
4 WISZ01 MESZ01 20252.964
5 MUSZ02 MESZ01 2989.984
6 MPSZ05 MESZ01 1431.330
7 WISZ03 MESZ01 19211.836
8 WISZ02 MESZ01 14960.942
9 SISZ02 MESZ01 7515.256
10 SISZ01 MESZ01 6391.342A constant value will be used to replace the intra-zonal distance that are 0. For that, I will uset he minimum distance. sumamry() will be used to find out what that value is.
# Check the minimum value of distance
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
MESZ01 : 331 MESZ01 : 331 Min. : 173.8
RVSZ05 : 331 RVSZ05 : 331 1st Qu.: 7149.5
SRSZ01 : 331 SRSZ01 : 331 Median :11890.0
WISZ01 : 331 WISZ01 : 331 Mean :12229.4
MUSZ02 : 331 MUSZ02 : 331 3rd Qu.:16401.7
MPSZ05 : 331 MPSZ05 : 331 Max. :49894.4
(Other):107906 (Other):107906 I’ll use a distance of 174m to the intra-zonal distance.
# Update distance pair
distPair$dist <- ifelse(distPair$dist == 0,
174, distPair$dist)
# Check result
summary(distPair) Var1 Var2 dist
MESZ01 : 332 MESZ01 : 332 Min. : 173.8
RVSZ05 : 332 RVSZ05 : 332 1st Qu.: 7097.3
SRSZ01 : 332 SRSZ01 : 332 Median :11863.7
WISZ01 : 332 WISZ01 : 332 Mean :12193.1
MUSZ02 : 332 MUSZ02 : 332 3rd Qu.:16387.7
MPSZ05 : 332 MPSZ05 : 332 Max. :49894.4
(Other):108232 (Other):108232 The final step is then to rename the columns into orig and dest.
# Rename columns
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)The result will be saved as rds
# Save output to rds
write_rds(distPair, "data/processed/distPair.rds")
# Read distPair from rds
distPair <- read_rds("data/processed/distPair.rds")16.3 Preparing Spatial Interaction Model (SIM) Data
In this section, I will prepare the SIM data for 16.4.
16.3.1 Preparing Flow Data
A few steps are required to prepare the flow data:
- Compute flow data (total passenger trip between and within planning subzones)
- Create additional flow attributes
- Combine passenger volume data with distance value
I’ll first load in the od_data created in 15.1.5.
# Load od_data_fii
od_data_fii <- read_rds("data/processed/od_data_fii.rds")To get the flow data, passenger trips (MORNING_PEAK) will be summed by ORIGIN_SZ (from) and DESTIN_SZ (to). Once done, I will check the flow_data dataframe.
flow_data <- od_data_fii %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(MORNING_PEAK)) `summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.# Check output
head(flow_data, 10)# A tibble: 10 × 3
# Groups: ORIGIN_SZ [1]
ORIGIN_SZ DESTIN_SZ TRIPS
<chr> <chr> <dbl>
1 AMSZ01 AMSZ01 2421
2 AMSZ01 AMSZ02 10201
3 AMSZ01 AMSZ03 14675
4 AMSZ01 AMSZ04 2892
5 AMSZ01 AMSZ05 7686
6 AMSZ01 AMSZ06 2374
7 AMSZ01 AMSZ07 1325
8 AMSZ01 AMSZ08 2593
9 AMSZ01 AMSZ09 2296
10 AMSZ01 AMSZ10 257Additional attributes will be created
- FlowNoIntra - remove all intra-region trips, coding them as 0 instead
- offset - set weights of intra-region trips to be very low (0.000001), and inter-region trips to be 1
# Create additional attributes
flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$TRIPS)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)Before joining the passenger volume data with distance pair, I need to convert the ORIGIN_SZ and DESTIN_SZ fields into factor data type. left_join will then be used to merge the 2 dataframes.
# Convert to factor data type
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)
# Join passenger volume dataframe to distance pair dataframe
flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))16.3.2 Preparing Origin and Destination Attributes
In this section, I will do further data processing to add demographics data. First, the population dataset will be read with read_csv() from readr package.
# Load population dataset
pop <- read_csv("data/aspatial/pop.csv")Rows: 332 Columns: 5
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): PA, SZ
dbl (3): AGE7_12, AGE13_24, AGE25_64
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Next, I will merge the population dataset with the mpsz sf dataframe to get population by subzone. The columns are renamed for better readability.
# Join population dataset with mpsz sf dataframe
pop <- pop %>%
left_join(mpsz,
by = c("PA" = "PLN_AREA_N",
"SZ" = "SUBZONE_N")) %>%
select(1:6) %>%
rename(SZ_NAME = SZ,
SZ = SUBZONE_C)Now, I will add the population data to the processed flow_data for both the origin (ORIGIN_SZ) and destination (DESTIN_SZ). The column names from population will be renamed to distinguish between origin and destination.
# Join population data to flow data on origin
flow_data1 <- flow_data1 %>%
left_join(pop,
by = c(ORIGIN_SZ = "SZ")) %>%
rename(ORIGIN_AGE7_12 = AGE7_12,
ORIGIN_AGE13_24 = AGE13_24,
ORIGIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))
# Join population data to flow data on destination
flow_data1 <- flow_data1 %>%
left_join(pop,
by = c(DESTIN_SZ = "SZ")) %>%
rename(DESTIN_AGE7_12 = AGE7_12,
DESTIN_AGE13_24 = AGE13_24,
DESTIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))Finally, this will be saved as rds format.
write_rds(flow_data1, "data/processed/SIM_data.rds")16.4 Calibrating Spatial Interaction Model
Lets load in the modelling data from 16.3.2.
# Load SIM data
SIM_data <- read_rds("data/processed/SIM_data.rds")16.4.1 Exploratory Data Analysis
It is always good to have a quick look at the data. I can view the distribution of the dependent variable (TRIPS) with a histogram.
# Visualize distribution of TRIPS
ggplot(data = SIM_data,
aes(x = TRIPS)) +
geom_histogram()`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
The distribution seems to be highly skewed and does not resemble a normal distribution. Next, I will visualize the relationship between the dependent variable and a key independent variable (distance).
# Visualize TRIPS vs dist
ggplot(data = SIM_data,
aes(x = dist,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
This relationship does not seem to resemble a linear relationship. However, if I were to use a log transformed version of both variables, it seems that they share a linear relationship.
# Visualize log TRIPS vs log distance
ggplot(data = SIM_data,
aes(x = log(dist),
y = log(TRIPS))) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
Given that Poisson Regression is based on log, I need to make sure that there are no 0 values (log(0) is undefined) in the independent variables. I can do that by checking the data with summary()
# Check SIM data distribution
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:21189 Length:21189 Min. : 1 Min. : 0.0
Class :character Class :character 1st Qu.: 16 1st Qu.: 14.0
Mode :character Mode :character Median : 84 Median : 77.0
Mean : 1113 Mean : 926.5
3rd Qu.: 435 3rd Qu.: 400.0
Max. :326696 Max. :201325.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :0.000001 Min. : 173.8 Min. : 0.0 Min. : 0
1st Qu.:1.000000 1st Qu.: 3377.2 1st Qu.: 50.0 1st Qu.: 100
Median :1.000000 Median : 6181.2 Median : 510.0 Median : 1130
Mean :0.986267 Mean : 7021.9 Mean : 885.8 Mean : 1948
3rd Qu.:1.000000 3rd Qu.: 9967.3 3rd Qu.:1360.0 3rd Qu.: 2950
Max. :1.000000 Max. :26135.8 Max. :6340.0 Max. :16380
ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0 Min. : 0.0 Min. : 0 Min. : 0
1st Qu.: 730 1st Qu.: 10.0 1st Qu.: 60 1st Qu.: 630
Median : 5710 Median : 510.0 Median : 1090 Median : 5640
Mean : 9064 Mean : 847.4 Mean : 1880 Mean : 8760
3rd Qu.:14180 3rd Qu.:1200.0 3rd Qu.: 2920 3rd Qu.:13650
Max. :74610 Max. :6340.0 Max. :16380 Max. :74610 From the summary report, ORIGIN_AGE7_12, ORIGIN_AGE13_24, ORIGIN_AGE25_64,DESTIN_AGE7_12, DESTIN_AGE13_24, DESTIN_AGE25_64 contains 0 values. Therefore, I will need to replace them with a small value (0.99). After that, summary() will be used to check the data again.
# Replace 0 value with 0.99
SIM_data$DESTIN_AGE7_12 <- ifelse(
SIM_data$DESTIN_AGE7_12 == 0,
0.99, SIM_data$DESTIN_AGE7_12)
SIM_data$DESTIN_AGE13_24 <- ifelse(
SIM_data$DESTIN_AGE13_24 == 0,
0.99, SIM_data$DESTIN_AGE13_24)
SIM_data$DESTIN_AGE25_64 <- ifelse(
SIM_data$DESTIN_AGE25_64 == 0,
0.99, SIM_data$DESTIN_AGE25_64)
SIM_data$ORIGIN_AGE7_12 <- ifelse(
SIM_data$ORIGIN_AGE7_12 == 0,
0.99, SIM_data$ORIGIN_AGE7_12)
SIM_data$ORIGIN_AGE13_24 <- ifelse(
SIM_data$ORIGIN_AGE13_24 == 0,
0.99, SIM_data$ORIGIN_AGE13_24)
SIM_data$ORIGIN_AGE25_64 <- ifelse(
SIM_data$ORIGIN_AGE25_64 == 0,
0.99, SIM_data$ORIGIN_AGE25_64)
# Check result
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:21189 Length:21189 Min. : 1 Min. : 0.0
Class :character Class :character 1st Qu.: 16 1st Qu.: 14.0
Mode :character Mode :character Median : 84 Median : 77.0
Mean : 1113 Mean : 926.5
3rd Qu.: 435 3rd Qu.: 400.0
Max. :326696 Max. :201325.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :0.000001 Min. : 173.8 Min. : 0.99 Min. : 0.99
1st Qu.:1.000000 1st Qu.: 3377.2 1st Qu.: 50.00 1st Qu.: 100.00
Median :1.000000 Median : 6181.2 Median : 510.00 Median : 1130.00
Mean :0.986267 Mean : 7021.9 Mean : 885.97 Mean : 1948.18
3rd Qu.:1.000000 3rd Qu.: 9967.3 3rd Qu.:1360.00 3rd Qu.: 2950.00
Max. :1.000000 Max. :26135.8 Max. :6340.00 Max. :16380.00
ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0.99 Min. : 0.99 Min. : 0.99 Min. : 0.99
1st Qu.: 730.00 1st Qu.: 10.00 1st Qu.: 60.00 1st Qu.: 630.00
Median : 5710.00 Median : 510.00 Median : 1090.00 Median : 5640.00
Mean : 9064.37 Mean : 847.64 Mean : 1880.59 Mean : 8760.31
3rd Qu.:14180.00 3rd Qu.:1200.00 3rd Qu.: 2920.00 3rd Qu.:13650.00
Max. :74610.00 Max. :6340.00 Max. :16380.00 Max. :74610.00 16.4.2 Unconstrained Spatial Interaction Model
Using glm() from base stats, I will calibrate an unconstrained spatial interaction model (SIM). The explanatory/independent variables used are origin population and destination population by different age cohort, and distance between origin and destination (in kilometre).
The general formula of the unconstrained SIM is as follows:
\[ \lambda_{ij} = \exp(k + \mu \ln V_i + \alpha \ln W_j - \beta \ln d_{ij}) \]
# Calibrate unconstrained SIM
uncSIM <- glm(formula = TRIPS ~
log(ORIGIN_AGE25_64) +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
# Check output
uncSIM
Call: glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) log(ORIGIN_AGE25_64) log(DESTIN_AGE25_64)
12.77060 0.27579 0.02557
log(dist)
-1.01728
Degrees of Freedom: 21188 Total (i.e. Null); 21185 Residual
Null Deviance: 100300000
Residual Deviance: 54440000 AIC: 54570000I will also create a R-square function to check how much variation of the trips the model can account for.
# Custom R square function
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Now, I will compute the R-square of the unconstrained SIM and compare it with the R-square of a generalized linear regression (using r2_macfadden() from performance package).
# Compute R square of unconstrained SIM
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)[1] 0.2192494# Compute R square of generalized linear regression
r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.457
adj. R2: 0.457Looks like the unconstrained SIM performs worse than a generalized linear regression model.
16.4.3 Origin (Production) constrained SIM
Using glm(), I will calibrate an origin constrained spatial interaction model (SIM). This is done by adding in origin (ORIGIN_SZ) as a independent variable.
The general formula of the origin constrained SIM is as follows:
\[ \lambda_{ij} = \exp(k + \mu_i + \alpha \ln W_j - \beta \ln d_{ij}) \]
# Calibrate origin constrained SIM
orcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
# Check output
summary(orcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(DESTIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.492e+01 3.308e-03 4508.112 < 2e-16 ***
ORIGIN_SZAMSZ02 9.973e-01 3.754e-03 265.667 < 2e-16 ***
ORIGIN_SZAMSZ03 6.095e-01 3.855e-03 158.102 < 2e-16 ***
ORIGIN_SZAMSZ04 -1.479e-03 4.364e-03 -0.339 0.7346
ORIGIN_SZAMSZ05 -1.896e-01 4.962e-03 -38.204 < 2e-16 ***
ORIGIN_SZAMSZ06 2.535e-01 4.482e-03 56.563 < 2e-16 ***
ORIGIN_SZAMSZ07 -1.133e+00 7.512e-03 -150.839 < 2e-16 ***
ORIGIN_SZAMSZ08 -8.104e-01 6.962e-03 -116.410 < 2e-16 ***
ORIGIN_SZAMSZ09 1.979e-01 4.617e-03 42.854 < 2e-16 ***
ORIGIN_SZAMSZ10 2.985e-01 4.251e-03 70.202 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.370e+00 9.049e-03 -151.457 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.558e+00 9.141e-03 -170.447 < 2e-16 ***
ORIGIN_SZBDSZ01 1.062e+00 3.729e-03 284.757 < 2e-16 ***
ORIGIN_SZBDSZ02 5.645e-01 4.293e-03 131.495 < 2e-16 ***
ORIGIN_SZBDSZ03 1.054e+00 3.812e-03 276.472 < 2e-16 ***
ORIGIN_SZBDSZ04 1.846e+00 3.337e-03 553.109 < 2e-16 ***
ORIGIN_SZBDSZ05 8.597e-01 3.788e-03 226.938 < 2e-16 ***
ORIGIN_SZBDSZ06 1.056e+00 3.829e-03 275.866 < 2e-16 ***
ORIGIN_SZBDSZ07 -8.060e-01 6.931e-03 -116.292 < 2e-16 ***
ORIGIN_SZBDSZ08 -7.434e-01 6.826e-03 -108.907 < 2e-16 ***
ORIGIN_SZBKSZ01 -3.244e-01 5.384e-03 -60.254 < 2e-16 ***
ORIGIN_SZBKSZ02 3.997e-01 4.324e-03 92.443 < 2e-16 ***
ORIGIN_SZBKSZ03 7.654e-01 4.008e-03 190.949 < 2e-16 ***
ORIGIN_SZBKSZ04 -1.974e-02 4.898e-03 -4.031 5.56e-05 ***
ORIGIN_SZBKSZ05 1.045e-01 4.586e-03 22.788 < 2e-16 ***
ORIGIN_SZBKSZ06 1.935e-02 4.929e-03 3.925 8.66e-05 ***
ORIGIN_SZBKSZ07 8.179e-01 3.723e-03 219.686 < 2e-16 ***
ORIGIN_SZBKSZ08 1.259e-01 4.406e-03 28.585 < 2e-16 ***
ORIGIN_SZBKSZ09 6.519e-02 4.622e-03 14.103 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.469e+00 1.079e-02 -136.119 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.171e+00 1.593e-02 -136.301 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.183e+00 3.190e-02 -99.765 < 2e-16 ***
ORIGIN_SZBLSZ04 -1.702e+00 1.494e-02 -113.956 < 2e-16 ***
ORIGIN_SZBMSZ01 2.872e-01 4.011e-03 71.587 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.199e+00 5.744e-03 -208.707 < 2e-16 ***
ORIGIN_SZBMSZ03 -3.828e-01 4.629e-03 -82.698 < 2e-16 ***
ORIGIN_SZBMSZ04 -1.266e-01 4.096e-03 -30.901 < 2e-16 ***
ORIGIN_SZBMSZ05 -1.378e+00 6.237e-03 -220.885 < 2e-16 ***
ORIGIN_SZBMSZ06 -1.872e+00 9.522e-03 -196.582 < 2e-16 ***
ORIGIN_SZBMSZ07 -3.887e-01 4.546e-03 -85.502 < 2e-16 ***
ORIGIN_SZBMSZ08 -5.320e-01 4.596e-03 -115.759 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.226e+00 5.876e-03 -208.654 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.310e+00 6.268e-03 -209.079 < 2e-16 ***
ORIGIN_SZBMSZ11 -9.506e-01 5.461e-03 -174.077 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.074e+00 6.895e-03 -155.712 < 2e-16 ***
ORIGIN_SZBMSZ13 -5.004e-02 4.515e-03 -11.084 < 2e-16 ***
ORIGIN_SZBMSZ14 -6.662e-01 5.376e-03 -123.922 < 2e-16 ***
ORIGIN_SZBMSZ15 -3.991e-01 4.869e-03 -81.984 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.314e+00 6.172e-03 -212.846 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.788e+00 9.456e-03 -189.063 < 2e-16 ***
ORIGIN_SZBPSZ01 2.174e-01 4.637e-03 46.888 < 2e-16 ***
ORIGIN_SZBPSZ02 1.113e-01 5.117e-03 21.755 < 2e-16 ***
ORIGIN_SZBPSZ03 3.970e-01 4.735e-03 83.837 < 2e-16 ***
ORIGIN_SZBPSZ04 5.318e-01 4.175e-03 127.377 < 2e-16 ***
ORIGIN_SZBPSZ05 6.193e-01 3.858e-03 160.529 < 2e-16 ***
ORIGIN_SZBPSZ06 -9.138e-01 6.708e-03 -136.222 < 2e-16 ***
ORIGIN_SZBPSZ07 -7.265e-01 6.617e-03 -109.789 < 2e-16 ***
ORIGIN_SZBSSZ01 4.647e-02 4.465e-03 10.408 < 2e-16 ***
ORIGIN_SZBSSZ02 4.311e-01 4.017e-03 107.327 < 2e-16 ***
ORIGIN_SZBSSZ03 2.857e-01 3.981e-03 71.755 < 2e-16 ***
ORIGIN_SZBTSZ01 1.890e-01 4.304e-03 43.908 < 2e-16 ***
ORIGIN_SZBTSZ02 -8.828e-01 6.292e-03 -140.318 < 2e-16 ***
ORIGIN_SZBTSZ03 3.561e-03 4.600e-03 0.774 0.4388
ORIGIN_SZBTSZ04 -7.815e-01 7.513e-03 -104.021 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.417e+00 8.631e-03 -164.200 < 2e-16 ***
ORIGIN_SZBTSZ06 -6.798e-01 5.862e-03 -115.982 < 2e-16 ***
ORIGIN_SZBTSZ07 -1.763e+00 8.554e-03 -206.102 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.063e+00 6.909e-03 -153.880 < 2e-16 ***
ORIGIN_SZCCSZ01 -1.489e+00 1.079e-02 -137.921 < 2e-16 ***
ORIGIN_SZCHSZ01 -1.026e+00 9.336e-03 -109.929 < 2e-16 ***
ORIGIN_SZCHSZ02 -6.286e-01 6.890e-03 -91.241 < 2e-16 ***
ORIGIN_SZCHSZ03 8.083e-01 4.663e-03 173.322 < 2e-16 ***
ORIGIN_SZCKSZ01 4.126e-01 4.147e-03 99.496 < 2e-16 ***
ORIGIN_SZCKSZ02 8.279e-01 4.160e-03 199.000 < 2e-16 ***
ORIGIN_SZCKSZ03 9.117e-01 3.803e-03 239.724 < 2e-16 ***
ORIGIN_SZCKSZ04 1.309e+00 3.867e-03 338.436 < 2e-16 ***
ORIGIN_SZCKSZ05 9.915e-01 4.463e-03 222.141 < 2e-16 ***
ORIGIN_SZCKSZ06 1.220e+00 4.268e-03 285.788 < 2e-16 ***
ORIGIN_SZCLSZ01 -3.506e-01 5.718e-03 -61.305 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.651e+00 1.086e-02 -151.973 < 2e-16 ***
ORIGIN_SZCLSZ03 -3.703e-01 5.399e-03 -68.588 < 2e-16 ***
ORIGIN_SZCLSZ04 8.543e-01 3.727e-03 229.221 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.667e+00 1.021e-02 -163.290 < 2e-16 ***
ORIGIN_SZCLSZ06 9.505e-01 3.558e-03 267.117 < 2e-16 ***
ORIGIN_SZCLSZ07 -7.409e-02 4.482e-03 -16.533 < 2e-16 ***
ORIGIN_SZCLSZ08 2.681e-01 4.917e-03 54.522 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.604e+00 1.286e-02 -124.717 < 2e-16 ***
ORIGIN_SZDTSZ01 -1.867e+00 7.108e-03 -262.653 < 2e-16 ***
ORIGIN_SZDTSZ02 -1.725e+00 6.715e-03 -256.852 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.100e+00 1.494e-02 -207.430 < 2e-16 ***
ORIGIN_SZDTSZ04 -4.545e+00 8.310e-02 -54.696 < 2e-16 ***
ORIGIN_SZDTSZ05 -3.438e+00 2.432e-02 -141.346 < 2e-16 ***
ORIGIN_SZDTSZ06 -3.224e+00 1.939e-02 -166.261 < 2e-16 ***
ORIGIN_SZDTSZ07 -2.240e+00 1.887e-02 -118.691 < 2e-16 ***
ORIGIN_SZDTSZ08 -2.377e+00 9.756e-03 -243.607 < 2e-16 ***
ORIGIN_SZDTSZ09 -3.293e+00 2.087e-02 -157.761 < 2e-16 ***
ORIGIN_SZDTSZ10 -2.281e+00 1.045e-02 -218.334 < 2e-16 ***
ORIGIN_SZDTSZ11 -2.377e+00 1.080e-02 -220.167 < 2e-16 ***
ORIGIN_SZDTSZ12 -3.703e+00 2.700e-02 -137.178 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.458e+00 1.257e-02 -195.471 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.350e+00 7.255e-03 -186.026 < 2e-16 ***
ORIGIN_SZGLSZ02 2.456e-01 4.149e-03 59.204 < 2e-16 ***
ORIGIN_SZGLSZ03 2.787e-01 4.127e-03 67.531 < 2e-16 ***
ORIGIN_SZGLSZ04 1.064e+00 3.478e-03 306.057 < 2e-16 ***
ORIGIN_SZGLSZ05 7.601e-01 3.694e-03 205.738 < 2e-16 ***
ORIGIN_SZHGSZ01 2.609e-01 4.093e-03 63.736 < 2e-16 ***
ORIGIN_SZHGSZ02 6.033e-01 3.921e-03 153.867 < 2e-16 ***
ORIGIN_SZHGSZ03 2.773e-01 4.310e-03 64.337 < 2e-16 ***
ORIGIN_SZHGSZ04 9.544e-01 3.661e-03 260.666 < 2e-16 ***
ORIGIN_SZHGSZ05 1.251e+00 3.601e-03 347.435 < 2e-16 ***
ORIGIN_SZHGSZ06 1.289e-01 4.345e-03 29.662 < 2e-16 ***
ORIGIN_SZHGSZ07 7.406e-01 3.784e-03 195.739 < 2e-16 ***
ORIGIN_SZHGSZ08 2.502e-01 4.341e-03 57.625 < 2e-16 ***
ORIGIN_SZHGSZ09 -6.254e-01 5.876e-03 -106.429 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.738e+00 3.856e-02 -96.960 < 2e-16 ***
ORIGIN_SZJESZ01 4.212e-01 4.162e-03 101.204 < 2e-16 ***
ORIGIN_SZJESZ02 2.463e-01 4.196e-03 58.715 < 2e-16 ***
ORIGIN_SZJESZ03 2.159e-01 4.419e-03 48.843 < 2e-16 ***
ORIGIN_SZJESZ04 -9.247e-01 6.955e-03 -132.955 < 2e-16 ***
ORIGIN_SZJESZ05 -2.094e+00 1.202e-02 -174.289 < 2e-16 ***
ORIGIN_SZJESZ06 3.880e-01 4.032e-03 96.242 < 2e-16 ***
ORIGIN_SZJESZ07 -1.706e+00 9.164e-03 -186.149 < 2e-16 ***
ORIGIN_SZJESZ08 -6.742e-01 8.277e-03 -81.453 < 2e-16 ***
ORIGIN_SZJESZ09 4.884e-01 4.288e-03 113.897 < 2e-16 ***
ORIGIN_SZJESZ10 -1.967e+00 1.661e-02 -118.380 < 2e-16 ***
ORIGIN_SZJESZ11 -1.960e+00 1.574e-02 -124.513 < 2e-16 ***
ORIGIN_SZJWSZ01 2.155e-01 5.535e-03 38.923 < 2e-16 ***
ORIGIN_SZJWSZ02 8.774e-01 3.872e-03 226.622 < 2e-16 ***
ORIGIN_SZJWSZ03 1.281e+00 3.597e-03 356.208 < 2e-16 ***
ORIGIN_SZJWSZ04 1.303e+00 3.662e-03 355.775 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.386e+00 1.029e-02 -134.681 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.036e+00 8.698e-03 -119.060 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.567e+00 2.130e-02 -120.517 < 2e-16 ***
ORIGIN_SZJWSZ08 1.939e+00 3.507e-03 552.937 < 2e-16 ***
ORIGIN_SZJWSZ09 1.986e+00 3.314e-03 599.270 < 2e-16 ***
ORIGIN_SZKLSZ01 2.098e-01 3.982e-03 52.698 < 2e-16 ***
ORIGIN_SZKLSZ02 -4.624e-01 4.965e-03 -93.122 < 2e-16 ***
ORIGIN_SZKLSZ03 -4.532e-01 4.989e-03 -90.839 < 2e-16 ***
ORIGIN_SZKLSZ04 -1.618e+00 6.990e-03 -231.532 < 2e-16 ***
ORIGIN_SZKLSZ05 -9.205e-01 6.637e-03 -138.693 < 2e-16 ***
ORIGIN_SZKLSZ06 -6.329e-01 4.650e-03 -136.125 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.030e+00 6.132e-03 -167.957 < 2e-16 ***
ORIGIN_SZKLSZ08 -8.334e-01 5.309e-03 -156.983 < 2e-16 ***
ORIGIN_SZKLSZ09 -1.617e+00 6.758e-03 -239.352 < 2e-16 ***
ORIGIN_SZLKSZ01 -3.116e+00 3.162e-02 -98.557 < 2e-16 ***
ORIGIN_SZMDSZ01 -2.337e+00 2.155e-02 -108.442 < 2e-16 ***
ORIGIN_SZMDSZ02 -1.184e+00 1.005e-02 -117.751 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.848e+00 1.329e-02 -139.034 < 2e-16 ***
ORIGIN_SZMPSZ01 -9.138e-01 6.558e-03 -139.351 < 2e-16 ***
ORIGIN_SZMPSZ02 -4.291e-01 5.472e-03 -78.427 < 2e-16 ***
ORIGIN_SZMPSZ03 2.287e-01 4.325e-03 52.885 < 2e-16 ***
ORIGIN_SZMSSZ01 -6.413e+00 3.780e-01 -16.966 < 2e-16 ***
ORIGIN_SZMUSZ01 -1.333e+00 5.854e-03 -227.763 < 2e-16 ***
ORIGIN_SZMUSZ02 -3.274e+00 1.446e-02 -226.445 < 2e-16 ***
ORIGIN_SZMUSZ03 -1.924e+00 6.893e-03 -279.052 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.341e+00 2.489e-02 -94.082 < 2e-16 ***
ORIGIN_SZNTSZ02 -2.554e+00 1.304e-02 -195.840 < 2e-16 ***
ORIGIN_SZNTSZ03 -8.610e-01 5.954e-03 -144.595 < 2e-16 ***
ORIGIN_SZNTSZ05 -3.240e+00 3.814e-02 -84.959 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.455e+00 3.797e-02 -90.992 < 2e-16 ***
ORIGIN_SZNVSZ01 6.612e-01 3.623e-03 182.497 < 2e-16 ***
ORIGIN_SZNVSZ02 -4.341e-01 4.874e-03 -89.069 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.085e+00 6.114e-03 -177.386 < 2e-16 ***
ORIGIN_SZNVSZ04 -1.242e+00 7.184e-03 -172.834 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.502e+00 1.339e-02 -186.817 < 2e-16 ***
ORIGIN_SZORSZ01 -3.296e+00 2.826e-02 -116.641 < 2e-16 ***
ORIGIN_SZORSZ02 -1.260e+00 5.814e-03 -216.668 < 2e-16 ***
ORIGIN_SZORSZ03 -1.730e+00 6.902e-03 -250.587 < 2e-16 ***
ORIGIN_SZOTSZ01 -1.800e+00 7.239e-03 -248.664 < 2e-16 ***
ORIGIN_SZOTSZ02 -1.868e+00 8.204e-03 -227.739 < 2e-16 ***
ORIGIN_SZOTSZ03 -9.620e-01 5.390e-03 -178.461 < 2e-16 ***
ORIGIN_SZOTSZ04 -8.109e-01 8.337e-03 -97.268 < 2e-16 ***
ORIGIN_SZPGSZ01 -7.269e-01 9.280e-03 -78.337 < 2e-16 ***
ORIGIN_SZPGSZ02 -3.518e-01 5.898e-03 -59.642 < 2e-16 ***
ORIGIN_SZPGSZ03 1.122e+00 3.724e-03 301.235 < 2e-16 ***
ORIGIN_SZPGSZ04 1.239e+00 3.722e-03 332.785 < 2e-16 ***
ORIGIN_SZPGSZ05 4.408e-01 4.647e-03 94.865 < 2e-16 ***
ORIGIN_SZPLSZ01 -5.569e-01 7.851e-03 -70.934 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.346e+00 1.116e-02 -120.587 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.949e+00 2.942e-02 -100.221 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.223e+00 3.088e-02 -104.351 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.259e+00 1.781e-02 -126.838 < 2e-16 ***
ORIGIN_SZPNSZ01 1.461e+00 3.902e-03 374.548 < 2e-16 ***
ORIGIN_SZPNSZ02 -6.115e-01 9.873e-03 -61.931 < 2e-16 ***
ORIGIN_SZPNSZ03 -1.988e+00 1.704e-02 -116.646 < 2e-16 ***
ORIGIN_SZPNSZ04 -2.678e+00 2.509e-02 -106.722 < 2e-16 ***
ORIGIN_SZPNSZ05 -1.837e+00 1.801e-02 -101.992 < 2e-16 ***
ORIGIN_SZPRSZ01 -7.978e-01 9.635e-03 -82.797 < 2e-16 ***
ORIGIN_SZPRSZ02 1.154e+00 3.874e-03 297.927 < 2e-16 ***
ORIGIN_SZPRSZ03 9.379e-01 3.872e-03 242.202 < 2e-16 ***
ORIGIN_SZPRSZ04 -2.384e-01 6.187e-03 -38.542 < 2e-16 ***
ORIGIN_SZPRSZ05 1.373e+00 3.701e-03 370.991 < 2e-16 ***
ORIGIN_SZPRSZ06 -4.211e-01 6.784e-03 -62.070 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.529e+00 1.662e-02 -152.170 < 2e-16 ***
ORIGIN_SZPRSZ08 1.661e-01 5.106e-03 32.534 < 2e-16 ***
ORIGIN_SZQTSZ01 -4.200e-01 5.459e-03 -76.939 < 2e-16 ***
ORIGIN_SZQTSZ02 -6.275e-01 5.072e-03 -123.710 < 2e-16 ***
ORIGIN_SZQTSZ03 -2.309e-01 4.724e-03 -48.878 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.030e+00 6.044e-03 -170.393 < 2e-16 ***
ORIGIN_SZQTSZ05 -2.498e-01 4.667e-03 -53.526 < 2e-16 ***
ORIGIN_SZQTSZ06 -5.085e-01 5.256e-03 -96.738 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.517e+00 7.888e-03 -192.362 < 2e-16 ***
ORIGIN_SZQTSZ08 -1.414e-01 4.706e-03 -30.039 < 2e-16 ***
ORIGIN_SZQTSZ09 -6.150e-01 5.571e-03 -110.406 < 2e-16 ***
ORIGIN_SZQTSZ10 -3.673e-01 5.312e-03 -69.147 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.240e+00 7.455e-03 -166.316 < 2e-16 ***
ORIGIN_SZQTSZ12 -6.568e-01 6.315e-03 -104.002 < 2e-16 ***
ORIGIN_SZQTSZ13 -1.766e-03 4.859e-03 -0.363 0.7163
ORIGIN_SZQTSZ14 -1.255e+00 7.114e-03 -176.406 < 2e-16 ***
ORIGIN_SZQTSZ15 -6.219e-01 8.141e-03 -76.396 < 2e-16 ***
ORIGIN_SZRCSZ01 -7.435e-01 5.320e-03 -139.774 < 2e-16 ***
ORIGIN_SZRCSZ02 -2.514e+00 1.573e-02 -159.805 < 2e-16 ***
ORIGIN_SZRCSZ03 -1.664e+00 7.375e-03 -225.655 < 2e-16 ***
ORIGIN_SZRCSZ04 -2.347e+00 1.108e-02 -211.743 < 2e-16 ***
ORIGIN_SZRCSZ05 -2.901e+00 1.372e-02 -211.521 < 2e-16 ***
ORIGIN_SZRCSZ06 -5.473e-01 7.118e-03 -76.900 < 2e-16 ***
ORIGIN_SZRCSZ08 -2.603e+00 1.616e-02 -161.101 < 2e-16 ***
ORIGIN_SZRCSZ09 -2.213e+00 1.235e-02 -179.166 < 2e-16 ***
ORIGIN_SZRCSZ10 -1.925e+00 7.010e-03 -274.597 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.838e+00 1.291e-02 -219.771 < 2e-16 ***
ORIGIN_SZRVSZ02 -1.313e+00 6.699e-03 -195.923 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.071e+00 9.651e-03 -214.634 < 2e-16 ***
ORIGIN_SZRVSZ04 -2.065e+00 1.386e-02 -148.974 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.294e+00 1.197e-02 -191.652 < 2e-16 ***
ORIGIN_SZSBSZ01 7.942e-01 4.441e-03 178.805 < 2e-16 ***
ORIGIN_SZSBSZ02 -5.518e-01 6.484e-03 -85.095 < 2e-16 ***
ORIGIN_SZSBSZ03 9.869e-01 3.927e-03 251.293 < 2e-16 ***
ORIGIN_SZSBSZ04 7.370e-01 4.459e-03 165.265 < 2e-16 ***
ORIGIN_SZSBSZ05 -1.074e-01 5.579e-03 -19.257 < 2e-16 ***
ORIGIN_SZSBSZ06 -1.693e+00 1.377e-02 -122.952 < 2e-16 ***
ORIGIN_SZSBSZ07 -7.681e-01 9.050e-03 -84.874 < 2e-16 ***
ORIGIN_SZSBSZ08 -1.024e+00 9.537e-03 -107.393 < 2e-16 ***
ORIGIN_SZSBSZ09 -4.906e-01 7.062e-03 -69.478 < 2e-16 ***
ORIGIN_SZSESZ02 1.147e+00 3.692e-03 310.686 < 2e-16 ***
ORIGIN_SZSESZ03 1.299e+00 3.540e-03 366.921 < 2e-16 ***
ORIGIN_SZSESZ04 9.358e-01 4.035e-03 231.934 < 2e-16 ***
ORIGIN_SZSESZ05 -1.812e-01 4.954e-03 -36.567 < 2e-16 ***
ORIGIN_SZSESZ06 9.649e-01 3.853e-03 250.392 < 2e-16 ***
ORIGIN_SZSESZ07 -2.172e+00 1.411e-02 -153.935 < 2e-16 ***
ORIGIN_SZSGSZ01 -8.624e-01 7.023e-03 -122.799 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.168e+00 8.296e-03 -140.773 < 2e-16 ***
ORIGIN_SZSGSZ03 2.736e-01 4.387e-03 62.367 < 2e-16 ***
ORIGIN_SZSGSZ04 3.981e-01 3.999e-03 99.544 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.679e+00 8.559e-03 -196.152 < 2e-16 ***
ORIGIN_SZSGSZ06 4.900e-01 3.832e-03 127.853 < 2e-16 ***
ORIGIN_SZSGSZ07 -5.267e-01 5.073e-03 -103.823 < 2e-16 ***
ORIGIN_SZSKSZ01 -9.897e-02 6.517e-03 -15.186 < 2e-16 ***
ORIGIN_SZSKSZ02 5.041e-01 4.773e-03 105.616 < 2e-16 ***
ORIGIN_SZSKSZ03 -3.733e-01 6.199e-03 -60.226 < 2e-16 ***
ORIGIN_SZSKSZ04 -2.368e+00 2.139e-02 -110.725 < 2e-16 ***
ORIGIN_SZSKSZ05 -1.261e+00 1.226e-02 -102.784 < 2e-16 ***
ORIGIN_SZSLSZ01 -3.224e+00 2.667e-02 -120.903 < 2e-16 ***
ORIGIN_SZSLSZ04 -3.092e-01 5.910e-03 -52.319 < 2e-16 ***
ORIGIN_SZSRSZ01 -1.626e+00 7.105e-03 -228.894 < 2e-16 ***
ORIGIN_SZSRSZ02 -1.867e+00 7.262e-03 -257.111 < 2e-16 ***
ORIGIN_SZSRSZ03 -3.003e+00 1.500e-02 -200.256 < 2e-16 ***
ORIGIN_SZSVSZ01 -2.784e+00 2.696e-02 -103.257 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.194e+00 4.519e-02 -48.550 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.577e+00 1.254e-02 -125.771 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.880e+00 2.385e-02 -120.729 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.633e+00 1.069e-02 -152.815 < 2e-16 ***
ORIGIN_SZTMSZ01 9.799e-01 4.179e-03 234.480 < 2e-16 ***
ORIGIN_SZTMSZ02 2.327e+00 3.246e-03 716.835 < 2e-16 ***
ORIGIN_SZTMSZ03 1.596e+00 3.466e-03 460.420 < 2e-16 ***
ORIGIN_SZTMSZ04 1.014e+00 3.981e-03 254.821 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.818e-01 6.281e-03 -28.948 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.100e+00 6.091e-03 -180.541 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.037e+00 5.744e-03 -180.467 < 2e-16 ***
ORIGIN_SZTNSZ03 -1.444e+00 7.342e-03 -196.638 < 2e-16 ***
ORIGIN_SZTNSZ04 -6.439e-01 5.568e-03 -115.639 < 2e-16 ***
ORIGIN_SZTPSZ01 -6.417e-01 5.261e-03 -121.956 < 2e-16 ***
ORIGIN_SZTPSZ02 5.001e-01 3.677e-03 136.004 < 2e-16 ***
ORIGIN_SZTPSZ03 -5.359e-01 5.273e-03 -101.613 < 2e-16 ***
ORIGIN_SZTPSZ04 -3.781e-01 4.909e-03 -77.033 < 2e-16 ***
ORIGIN_SZTPSZ05 -3.393e-01 5.068e-03 -66.957 < 2e-16 ***
ORIGIN_SZTPSZ06 4.384e-02 5.078e-03 8.633 < 2e-16 ***
ORIGIN_SZTPSZ07 -2.999e-01 5.087e-03 -58.961 < 2e-16 ***
ORIGIN_SZTPSZ08 -7.527e-01 6.706e-03 -112.244 < 2e-16 ***
ORIGIN_SZTPSZ09 -5.025e-01 5.393e-03 -93.162 < 2e-16 ***
ORIGIN_SZTPSZ10 -4.239e-01 5.472e-03 -77.462 < 2e-16 ***
ORIGIN_SZTPSZ11 1.840e-01 4.291e-03 42.869 < 2e-16 ***
ORIGIN_SZTPSZ12 -5.342e-01 5.392e-03 -99.061 < 2e-16 ***
ORIGIN_SZTSSZ01 -3.439e+00 3.996e-02 -86.045 < 2e-16 ***
ORIGIN_SZTSSZ02 5.225e-01 5.839e-03 89.484 < 2e-16 ***
ORIGIN_SZTSSZ03 4.400e-01 5.870e-03 74.956 < 2e-16 ***
ORIGIN_SZTSSZ04 4.226e-01 6.193e-03 68.235 < 2e-16 ***
ORIGIN_SZTSSZ05 -9.305e-01 1.118e-02 -83.212 < 2e-16 ***
ORIGIN_SZTSSZ06 -1.150e+00 1.372e-02 -83.825 < 2e-16 ***
ORIGIN_SZWCSZ01 3.935e-01 5.706e-03 68.962 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.855e+00 2.539e-02 -112.419 < 2e-16 ***
ORIGIN_SZWCSZ03 -4.541e+00 1.187e-01 -38.254 < 2e-16 ***
ORIGIN_SZWDSZ01 1.437e+00 3.554e-03 404.310 < 2e-16 ***
ORIGIN_SZWDSZ02 1.062e+00 4.013e-03 264.616 < 2e-16 ***
ORIGIN_SZWDSZ03 2.180e+00 3.429e-03 635.604 < 2e-16 ***
ORIGIN_SZWDSZ04 1.175e+00 4.195e-03 280.228 < 2e-16 ***
ORIGIN_SZWDSZ05 7.164e-01 4.208e-03 170.254 < 2e-16 ***
ORIGIN_SZWDSZ06 1.280e+00 3.883e-03 329.648 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.453e-02 5.857e-03 -2.480 0.0131 *
ORIGIN_SZWDSZ08 -3.921e-01 6.666e-03 -58.828 < 2e-16 ***
ORIGIN_SZWDSZ09 1.773e+00 3.587e-03 494.384 < 2e-16 ***
ORIGIN_SZYSSZ01 -3.142e-02 4.762e-03 -6.598 4.17e-11 ***
ORIGIN_SZYSSZ02 8.925e-01 4.236e-03 210.677 < 2e-16 ***
ORIGIN_SZYSSZ03 1.856e+00 3.536e-03 524.915 < 2e-16 ***
ORIGIN_SZYSSZ04 9.673e-01 3.793e-03 255.015 < 2e-16 ***
ORIGIN_SZYSSZ05 2.627e-01 4.667e-03 56.298 < 2e-16 ***
ORIGIN_SZYSSZ06 -6.909e-01 7.531e-03 -91.734 < 2e-16 ***
ORIGIN_SZYSSZ07 -6.578e-01 7.588e-03 -86.687 < 2e-16 ***
ORIGIN_SZYSSZ08 -3.432e-02 5.264e-03 -6.519 7.06e-11 ***
ORIGIN_SZYSSZ09 1.375e+00 3.641e-03 377.806 < 2e-16 ***
log(DESTIN_AGE25_64) 2.059e-02 6.755e-05 304.776 < 2e-16 ***
log(dist) -1.009e+00 1.439e-04 -7010.995 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 100298738 on 21188 degrees of freedom
Residual deviance: 38254249 on 20878 degrees of freedom
AIC: 38388198
Number of Fisher Scoring iterations: 7With the previously created function, I can compute the R-sqaure for this model.
# Compute R square of origin constrained SIM
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)[1] 0.4332865It is much better than unconstrained SIM but is still slightly worse than the generalised linear regression of 0.457.
16.4.4 Destination (Attraction) constrained SIM
To calibrate the destination constrained SIM, I will need to flip the independent variables as compared to origin constrained SIM, using destination (DESTIN_SZ) instead of origin (ORIGIN_SZ) and likewise log(ORIGIN_AG25_64) instead of log(DEST_AGE_25-64).
The general formula of destination constrained SIM is as follows:
\[ \lambda_{ij} = \exp(k + \mu \ln V_i + \alpha_i - \beta \ln d_{ij}) \]
# Calibrate destination constrained SIM
decSIM <- glm(formula = TRIPS ~
DESTIN_SZ +
log(ORIGIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
# Check output
summary(decSIM)
Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 13.5319761 0.0029234 4628.775 < 2e-16 ***
DESTIN_SZAMSZ02 0.0167918 0.0037928 4.427 9.54e-06 ***
DESTIN_SZAMSZ03 0.2319475 0.0035339 65.635 < 2e-16 ***
DESTIN_SZAMSZ04 -0.9975760 0.0053076 -187.954 < 2e-16 ***
DESTIN_SZAMSZ05 -0.9817146 0.0050484 -194.460 < 2e-16 ***
DESTIN_SZAMSZ06 -0.8013764 0.0048434 -165.458 < 2e-16 ***
DESTIN_SZAMSZ07 -1.8664277 0.0087108 -214.267 < 2e-16 ***
DESTIN_SZAMSZ08 -0.8455618 0.0054125 -156.223 < 2e-16 ***
DESTIN_SZAMSZ09 -0.9892781 0.0052646 -187.910 < 2e-16 ***
DESTIN_SZAMSZ10 0.4506862 0.0036043 125.042 < 2e-16 ***
DESTIN_SZAMSZ11 0.1180698 0.0059975 19.686 < 2e-16 ***
DESTIN_SZAMSZ12 -0.7865942 0.0058220 -135.107 < 2e-16 ***
DESTIN_SZBDSZ01 0.6130392 0.0032390 189.269 < 2e-16 ***
DESTIN_SZBDSZ02 -0.1227433 0.0041344 -29.688 < 2e-16 ***
DESTIN_SZBDSZ03 0.1227126 0.0036407 33.706 < 2e-16 ***
DESTIN_SZBDSZ04 1.1293528 0.0029731 379.851 < 2e-16 ***
DESTIN_SZBDSZ05 0.5334000 0.0033123 161.037 < 2e-16 ***
DESTIN_SZBDSZ06 0.1898257 0.0037326 50.857 < 2e-16 ***
DESTIN_SZBDSZ07 -0.9767668 0.0075882 -128.722 < 2e-16 ***
DESTIN_SZBDSZ08 -1.2776183 0.0074432 -171.650 < 2e-16 ***
DESTIN_SZBKSZ01 -1.1543861 0.0056246 -205.238 < 2e-16 ***
DESTIN_SZBKSZ02 -0.2799558 0.0044888 -62.368 < 2e-16 ***
DESTIN_SZBKSZ03 -0.4163999 0.0044282 -94.033 < 2e-16 ***
DESTIN_SZBKSZ04 -0.0433921 0.0040333 -10.759 < 2e-16 ***
DESTIN_SZBKSZ05 -0.5599078 0.0045187 -123.909 < 2e-16 ***
DESTIN_SZBKSZ06 -0.8025541 0.0050323 -159.480 < 2e-16 ***
DESTIN_SZBKSZ07 0.2522082 0.0034407 73.302 < 2e-16 ***
DESTIN_SZBKSZ08 -1.0727218 0.0057334 -187.101 < 2e-16 ***
DESTIN_SZBKSZ09 -0.2082187 0.0041030 -50.748 < 2e-16 ***
DESTIN_SZBLSZ01 -0.2954183 0.0059378 -49.752 < 2e-16 ***
DESTIN_SZBLSZ02 0.6603094 0.0056115 117.671 < 2e-16 ***
DESTIN_SZBLSZ03 1.5311975 0.0060045 255.006 < 2e-16 ***
DESTIN_SZBLSZ04 0.0147093 0.0112063 1.313 0.1893
DESTIN_SZBMSZ01 -0.0207789 0.0037348 -5.564 2.64e-08 ***
DESTIN_SZBMSZ02 -0.4894000 0.0039318 -124.472 < 2e-16 ***
DESTIN_SZBMSZ03 -0.9557338 0.0048392 -197.500 < 2e-16 ***
DESTIN_SZBMSZ04 -0.6736138 0.0041564 -162.068 < 2e-16 ***
DESTIN_SZBMSZ05 -0.6134023 0.0049484 -123.959 < 2e-16 ***
DESTIN_SZBMSZ06 -1.7744760 0.0086211 -205.830 < 2e-16 ***
DESTIN_SZBMSZ07 -0.1191551 0.0036709 -32.459 < 2e-16 ***
DESTIN_SZBMSZ08 -1.1864022 0.0048790 -243.163 < 2e-16 ***
DESTIN_SZBMSZ09 -2.0825468 0.0075855 -274.545 < 2e-16 ***
DESTIN_SZBMSZ10 -1.6320024 0.0060450 -269.975 < 2e-16 ***
DESTIN_SZBMSZ11 -1.6324610 0.0060813 -268.438 < 2e-16 ***
DESTIN_SZBMSZ12 -1.0218241 0.0059304 -172.304 < 2e-16 ***
DESTIN_SZBMSZ13 -0.1855890 0.0038762 -47.879 < 2e-16 ***
DESTIN_SZBMSZ14 -1.2235957 0.0062318 -196.348 < 2e-16 ***
DESTIN_SZBMSZ15 -1.3667495 0.0059462 -229.852 < 2e-16 ***
DESTIN_SZBMSZ16 -1.5756133 0.0061364 -256.765 < 2e-16 ***
DESTIN_SZBMSZ17 -1.4423702 0.0072796 -198.138 < 2e-16 ***
DESTIN_SZBPSZ01 -0.5244651 0.0044773 -117.140 < 2e-16 ***
DESTIN_SZBPSZ02 -1.6486894 0.0075109 -219.506 < 2e-16 ***
DESTIN_SZBPSZ03 -1.3000214 0.0068596 -189.518 < 2e-16 ***
DESTIN_SZBPSZ04 -0.6795349 0.0050062 -135.738 < 2e-16 ***
DESTIN_SZBPSZ05 0.5710966 0.0032576 175.311 < 2e-16 ***
DESTIN_SZBPSZ06 -0.7993487 0.0061090 -130.848 < 2e-16 ***
DESTIN_SZBPSZ07 -0.5306457 0.0062665 -84.680 < 2e-16 ***
DESTIN_SZBSSZ01 -0.1419229 0.0038218 -37.135 < 2e-16 ***
DESTIN_SZBSSZ02 -0.7491614 0.0044259 -169.268 < 2e-16 ***
DESTIN_SZBSSZ03 0.3015135 0.0032333 93.253 < 2e-16 ***
DESTIN_SZBTSZ01 0.2441227 0.0034925 69.900 < 2e-16 ***
DESTIN_SZBTSZ02 -0.5993334 0.0054119 -110.744 < 2e-16 ***
DESTIN_SZBTSZ03 -0.1722937 0.0041744 -41.274 < 2e-16 ***
DESTIN_SZBTSZ04 -1.5617992 0.0080789 -193.317 < 2e-16 ***
DESTIN_SZBTSZ05 -0.7599773 0.0058902 -129.023 < 2e-16 ***
DESTIN_SZBTSZ06 -0.8605287 0.0052281 -164.596 < 2e-16 ***
DESTIN_SZBTSZ07 -1.8942101 0.0078748 -240.541 < 2e-16 ***
DESTIN_SZBTSZ08 -1.2820702 0.0068844 -186.228 < 2e-16 ***
DESTIN_SZCCSZ01 -0.4160366 0.0058077 -71.635 < 2e-16 ***
DESTIN_SZCHSZ01 -0.8537149 0.0073861 -115.584 < 2e-16 ***
DESTIN_SZCHSZ02 0.0405302 0.0046186 8.775 < 2e-16 ***
DESTIN_SZCHSZ03 2.0014354 0.0032285 619.928 < 2e-16 ***
DESTIN_SZCKSZ01 -0.2572841 0.0042162 -61.022 < 2e-16 ***
DESTIN_SZCKSZ02 -0.6566890 0.0048095 -136.541 < 2e-16 ***
DESTIN_SZCKSZ03 0.6866678 0.0032915 208.622 < 2e-16 ***
DESTIN_SZCKSZ04 -0.6872999 0.0052477 -130.971 < 2e-16 ***
DESTIN_SZCKSZ05 -0.4977357 0.0056110 -88.707 < 2e-16 ***
DESTIN_SZCKSZ06 0.7099744 0.0038346 185.149 < 2e-16 ***
DESTIN_SZCLSZ01 0.4611783 0.0039429 116.965 < 2e-16 ***
DESTIN_SZCLSZ02 -2.2149750 0.0108205 -204.702 < 2e-16 ***
DESTIN_SZCLSZ03 -1.0099330 0.0061938 -163.056 < 2e-16 ***
DESTIN_SZCLSZ04 0.1446405 0.0036400 39.736 < 2e-16 ***
DESTIN_SZCLSZ05 -1.1992262 0.0069904 -171.552 < 2e-16 ***
DESTIN_SZCLSZ06 0.2630380 0.0034203 76.904 < 2e-16 ***
DESTIN_SZCLSZ07 -0.5626895 0.0044296 -127.029 < 2e-16 ***
DESTIN_SZCLSZ08 -0.4318994 0.0049237 -87.718 < 2e-16 ***
DESTIN_SZCLSZ09 0.3225340 0.0055773 57.830 < 2e-16 ***
DESTIN_SZDTSZ01 -0.8829222 0.0044509 -198.371 < 2e-16 ***
DESTIN_SZDTSZ02 -0.7893793 0.0043900 -179.812 < 2e-16 ***
DESTIN_SZDTSZ03 -1.1406915 0.0055817 -204.362 < 2e-16 ***
DESTIN_SZDTSZ04 -2.1711734 0.0105297 -206.196 < 2e-16 ***
DESTIN_SZDTSZ05 -1.2397874 0.0093084 -133.191 < 2e-16 ***
DESTIN_SZDTSZ06 -1.2331107 0.0063241 -194.985 < 2e-16 ***
DESTIN_SZDTSZ07 -1.9364999 0.0183439 -105.567 < 2e-16 ***
DESTIN_SZDTSZ08 -0.6054414 0.0042494 -142.478 < 2e-16 ***
DESTIN_SZDTSZ09 -1.4039196 0.0092265 -152.162 < 2e-16 ***
DESTIN_SZDTSZ10 -1.3289214 0.0074586 -178.172 < 2e-16 ***
DESTIN_SZDTSZ11 -0.7402263 0.0045670 -162.080 < 2e-16 ***
DESTIN_SZDTSZ12 -2.3295417 0.0147971 -157.432 < 2e-16 ***
DESTIN_SZDTSZ13 -2.0315184 0.0094796 -214.303 < 2e-16 ***
DESTIN_SZGLSZ01 -0.0092902 0.0041980 -2.213 0.0269 *
DESTIN_SZGLSZ02 -0.2705099 0.0038799 -69.721 < 2e-16 ***
DESTIN_SZGLSZ03 0.4947169 0.0032749 151.063 < 2e-16 ***
DESTIN_SZGLSZ04 0.4703262 0.0031938 147.262 < 2e-16 ***
DESTIN_SZGLSZ05 0.2433273 0.0033787 72.019 < 2e-16 ***
DESTIN_SZHGSZ01 0.4393639 0.0032561 134.935 < 2e-16 ***
DESTIN_SZHGSZ02 -0.6231353 0.0045295 -137.572 < 2e-16 ***
DESTIN_SZHGSZ03 -1.1574609 0.0054926 -210.729 < 2e-16 ***
DESTIN_SZHGSZ04 -0.2928319 0.0038420 -76.218 < 2e-16 ***
DESTIN_SZHGSZ05 -0.1755917 0.0038295 -45.852 < 2e-16 ***
DESTIN_SZHGSZ06 -0.6984402 0.0045154 -154.679 < 2e-16 ***
DESTIN_SZHGSZ07 0.2697113 0.0034511 78.152 < 2e-16 ***
DESTIN_SZHGSZ08 -0.2343835 0.0040315 -58.138 < 2e-16 ***
DESTIN_SZHGSZ09 0.2484051 0.0042082 59.029 < 2e-16 ***
DESTIN_SZHGSZ10 -3.4695547 0.0288974 -120.065 < 2e-16 ***
DESTIN_SZJESZ01 -0.1338640 0.0042003 -31.870 < 2e-16 ***
DESTIN_SZJESZ02 -0.4614152 0.0043445 -106.207 < 2e-16 ***
DESTIN_SZJESZ03 -0.5684334 0.0047021 -120.890 < 2e-16 ***
DESTIN_SZJESZ04 -0.1238527 0.0049662 -24.939 < 2e-16 ***
DESTIN_SZJESZ05 -0.7647843 0.0074365 -102.843 < 2e-16 ***
DESTIN_SZJESZ06 0.4355935 0.0034536 126.126 < 2e-16 ***
DESTIN_SZJESZ07 -0.8567853 0.0061617 -139.050 < 2e-16 ***
DESTIN_SZJESZ08 -0.4251726 0.0064345 -66.077 < 2e-16 ***
DESTIN_SZJESZ09 -0.3604438 0.0047713 -75.544 < 2e-16 ***
DESTIN_SZJESZ10 0.7220157 0.0062503 115.518 < 2e-16 ***
DESTIN_SZJESZ11 0.9659224 0.0055256 174.809 < 2e-16 ***
DESTIN_SZJWSZ01 -0.3904071 0.0054402 -71.763 < 2e-16 ***
DESTIN_SZJWSZ02 -0.3722923 0.0045833 -81.229 < 2e-16 ***
DESTIN_SZJWSZ03 0.5996900 0.0034496 173.845 < 2e-16 ***
DESTIN_SZJWSZ04 0.9929145 0.0032104 309.282 < 2e-16 ***
DESTIN_SZJWSZ05 -0.2417404 0.0051383 -47.047 < 2e-16 ***
DESTIN_SZJWSZ06 0.3734233 0.0046335 80.592 < 2e-16 ***
DESTIN_SZJWSZ07 -0.6990202 0.0189832 -36.823 < 2e-16 ***
DESTIN_SZJWSZ08 0.4180364 0.0039024 107.124 < 2e-16 ***
DESTIN_SZJWSZ09 1.5196041 0.0029079 522.571 < 2e-16 ***
DESTIN_SZKLSZ01 -0.6012425 0.0041149 -146.113 < 2e-16 ***
DESTIN_SZKLSZ02 -0.7885356 0.0047111 -167.377 < 2e-16 ***
DESTIN_SZKLSZ03 -1.1966684 0.0051723 -231.359 < 2e-16 ***
DESTIN_SZKLSZ04 -1.6837636 0.0066518 -253.131 < 2e-16 ***
DESTIN_SZKLSZ05 -1.1121267 0.0068381 -162.636 < 2e-16 ***
DESTIN_SZKLSZ06 -0.8994778 0.0044837 -200.611 < 2e-16 ***
DESTIN_SZKLSZ07 -1.0722167 0.0051024 -210.139 < 2e-16 ***
DESTIN_SZKLSZ08 -0.1040235 0.0036799 -28.268 < 2e-16 ***
DESTIN_SZKLSZ09 -1.8028528 0.0066500 -271.106 < 2e-16 ***
DESTIN_SZLKSZ01 -1.5666862 0.0197773 -79.217 < 2e-16 ***
DESTIN_SZMDSZ01 -1.3118968 0.0160120 -81.932 < 2e-16 ***
DESTIN_SZMDSZ02 -1.1030330 0.0095009 -116.098 < 2e-16 ***
DESTIN_SZMDSZ03 -2.7327519 0.0212751 -128.449 < 2e-16 ***
DESTIN_SZMPSZ01 -1.2239529 0.0066157 -185.006 < 2e-16 ***
DESTIN_SZMPSZ02 -0.8082708 0.0049437 -163.494 < 2e-16 ***
DESTIN_SZMPSZ03 -0.1228211 0.0039989 -30.714 < 2e-16 ***
DESTIN_SZMSSZ01 -3.3362771 0.0747877 -44.610 < 2e-16 ***
DESTIN_SZMUSZ01 -1.0789799 0.0048487 -222.532 < 2e-16 ***
DESTIN_SZMUSZ02 -1.4951866 0.0069812 -214.173 < 2e-16 ***
DESTIN_SZMUSZ03 -1.0259562 0.0047088 -217.881 < 2e-16 ***
DESTIN_SZNTSZ01 -2.8190222 0.0210582 -133.868 < 2e-16 ***
DESTIN_SZNTSZ02 -2.1008370 0.0090816 -231.328 < 2e-16 ***
DESTIN_SZNTSZ03 -1.2160830 0.0060652 -200.502 < 2e-16 ***
DESTIN_SZNTSZ05 -1.7901223 0.0165652 -108.065 < 2e-16 ***
DESTIN_SZNTSZ06 -2.9970912 0.0274278 -109.272 < 2e-16 ***
DESTIN_SZNVSZ01 -0.2390833 0.0036171 -66.098 < 2e-16 ***
DESTIN_SZNVSZ02 -0.4540187 0.0041346 -109.808 < 2e-16 ***
DESTIN_SZNVSZ03 -0.5806739 0.0044606 -130.178 < 2e-16 ***
DESTIN_SZNVSZ04 -2.0062112 0.0085263 -235.296 < 2e-16 ***
DESTIN_SZNVSZ05 -1.8981580 0.0077725 -244.215 < 2e-16 ***
DESTIN_SZORSZ01 -2.2557576 0.0176246 -127.989 < 2e-16 ***
DESTIN_SZORSZ02 -0.0902313 0.0036934 -24.430 < 2e-16 ***
DESTIN_SZORSZ03 -0.8661247 0.0047631 -181.841 < 2e-16 ***
DESTIN_SZOTSZ01 -1.6401146 0.0061714 -265.759 < 2e-16 ***
DESTIN_SZOTSZ02 -0.9007565 0.0053437 -168.563 < 2e-16 ***
DESTIN_SZOTSZ03 -1.4600248 0.0056500 -258.412 < 2e-16 ***
DESTIN_SZOTSZ04 -1.5153965 0.0083258 -182.012 < 2e-16 ***
DESTIN_SZPGSZ01 -2.1550984 0.0140910 -152.942 < 2e-16 ***
DESTIN_SZPGSZ02 -0.8145229 0.0055203 -147.552 < 2e-16 ***
DESTIN_SZPGSZ03 0.5947295 0.0033010 180.165 < 2e-16 ***
DESTIN_SZPGSZ04 0.0952627 0.0037662 25.294 < 2e-16 ***
DESTIN_SZPGSZ05 -0.9740800 0.0061999 -157.112 < 2e-16 ***
DESTIN_SZPLSZ01 -0.0143705 0.0059088 -2.432 0.0150 *
DESTIN_SZPLSZ02 -1.1215894 0.0100665 -111.418 < 2e-16 ***
DESTIN_SZPLSZ03 -0.1264989 0.0082183 -15.392 < 2e-16 ***
DESTIN_SZPLSZ04 -0.2164306 0.0076017 -28.471 < 2e-16 ***
DESTIN_SZPLSZ05 -0.7193772 0.0097102 -74.085 < 2e-16 ***
DESTIN_SZPNSZ01 1.2424880 0.0042508 292.298 < 2e-16 ***
DESTIN_SZPNSZ02 1.6609442 0.0056322 294.901 < 2e-16 ***
DESTIN_SZPNSZ03 0.9245230 0.0064359 143.651 < 2e-16 ***
DESTIN_SZPNSZ04 1.7379655 0.0064485 269.515 < 2e-16 ***
DESTIN_SZPNSZ05 0.9316803 0.0092764 100.435 < 2e-16 ***
DESTIN_SZPRSZ01 -0.5598464 0.0061652 -90.807 < 2e-16 ***
DESTIN_SZPRSZ02 -0.1007064 0.0042331 -23.790 < 2e-16 ***
DESTIN_SZPRSZ03 0.8446501 0.0031869 265.040 < 2e-16 ***
DESTIN_SZPRSZ04 -0.7023098 0.0069327 -101.305 < 2e-16 ***
DESTIN_SZPRSZ05 -0.0059708 0.0039934 -1.495 0.1349
DESTIN_SZPRSZ06 0.5972882 0.0041480 143.994 < 2e-16 ***
DESTIN_SZPRSZ07 -1.5960113 0.0103536 -154.151 < 2e-16 ***
DESTIN_SZPRSZ08 -0.7301565 0.0056082 -130.194 < 2e-16 ***
DESTIN_SZQTSZ01 -1.4502101 0.0079905 -181.492 < 2e-16 ***
DESTIN_SZQTSZ02 -1.2813349 0.0057647 -222.274 < 2e-16 ***
DESTIN_SZQTSZ03 -0.8708814 0.0052594 -165.584 < 2e-16 ***
DESTIN_SZQTSZ04 -1.0902881 0.0054843 -198.801 < 2e-16 ***
DESTIN_SZQTSZ05 -0.9588636 0.0048988 -195.733 < 2e-16 ***
DESTIN_SZQTSZ06 -1.2011542 0.0053168 -225.918 < 2e-16 ***
DESTIN_SZQTSZ07 -1.6371435 0.0088569 -184.843 < 2e-16 ***
DESTIN_SZQTSZ08 0.1925489 0.0037467 51.392 < 2e-16 ***
DESTIN_SZQTSZ09 -0.4411194 0.0048083 -91.741 < 2e-16 ***
DESTIN_SZQTSZ10 -0.2479036 0.0042113 -58.866 < 2e-16 ***
DESTIN_SZQTSZ11 0.3026852 0.0040142 75.404 < 2e-16 ***
DESTIN_SZQTSZ12 -0.2864852 0.0052343 -54.732 < 2e-16 ***
DESTIN_SZQTSZ13 0.2341588 0.0039646 59.062 < 2e-16 ***
DESTIN_SZQTSZ14 -0.0003169 0.0044237 -0.072 0.9429
DESTIN_SZQTSZ15 0.2798212 0.0054385 51.452 < 2e-16 ***
DESTIN_SZRCSZ01 -1.0655438 0.0052103 -204.505 < 2e-16 ***
DESTIN_SZRCSZ02 -2.2412920 0.0134860 -166.194 < 2e-16 ***
DESTIN_SZRCSZ03 -1.0931496 0.0070796 -154.408 < 2e-16 ***
DESTIN_SZRCSZ04 -2.7083784 0.0107670 -251.543 < 2e-16 ***
DESTIN_SZRCSZ05 -2.4072719 0.0096294 -249.991 < 2e-16 ***
DESTIN_SZRCSZ06 -2.2079454 0.0122381 -180.416 < 2e-16 ***
DESTIN_SZRCSZ08 -2.2845085 0.0101601 -224.851 < 2e-16 ***
DESTIN_SZRCSZ09 -1.7033647 0.0093982 -181.244 < 2e-16 ***
DESTIN_SZRCSZ10 -1.1179258 0.0050257 -222.441 < 2e-16 ***
DESTIN_SZRVSZ01 -2.2094685 0.0087506 -252.493 < 2e-16 ***
DESTIN_SZRVSZ02 -2.5316202 0.0118374 -213.867 < 2e-16 ***
DESTIN_SZRVSZ03 -2.5227530 0.0103503 -243.737 < 2e-16 ***
DESTIN_SZRVSZ04 -1.8936058 0.0118022 -160.445 < 2e-16 ***
DESTIN_SZRVSZ05 -2.2591957 0.0111171 -203.218 < 2e-16 ***
DESTIN_SZSBSZ01 -0.1468109 0.0046757 -31.399 < 2e-16 ***
DESTIN_SZSBSZ02 -0.9746248 0.0059588 -163.561 < 2e-16 ***
DESTIN_SZSBSZ03 0.6352135 0.0034932 181.843 < 2e-16 ***
DESTIN_SZSBSZ04 0.0743888 0.0045091 16.498 < 2e-16 ***
DESTIN_SZSBSZ05 -0.8413827 0.0057920 -145.267 < 2e-16 ***
DESTIN_SZSBSZ06 -2.6495895 0.0219836 -120.526 < 2e-16 ***
DESTIN_SZSBSZ07 -0.6527664 0.0155913 -41.867 < 2e-16 ***
DESTIN_SZSBSZ08 1.5182976 0.0041938 362.031 < 2e-16 ***
DESTIN_SZSBSZ09 0.7935678 0.0041526 191.101 < 2e-16 ***
DESTIN_SZSESZ02 -0.1621119 0.0039540 -40.999 < 2e-16 ***
DESTIN_SZSESZ03 0.7066748 0.0031165 226.756 < 2e-16 ***
DESTIN_SZSESZ04 -0.5750009 0.0045086 -127.535 < 2e-16 ***
DESTIN_SZSESZ05 -0.1565752 0.0038440 -40.733 < 2e-16 ***
DESTIN_SZSESZ06 -0.5096637 0.0047839 -106.537 < 2e-16 ***
DESTIN_SZSESZ07 -2.7566947 0.0193270 -142.635 < 2e-16 ***
DESTIN_SZSGSZ01 -0.3909858 0.0048459 -80.684 < 2e-16 ***
DESTIN_SZSGSZ02 0.0853309 0.0042688 19.989 < 2e-16 ***
DESTIN_SZSGSZ03 -0.3550648 0.0040795 -87.037 < 2e-16 ***
DESTIN_SZSGSZ04 -0.2303256 0.0039377 -58.492 < 2e-16 ***
DESTIN_SZSGSZ05 -2.0837963 0.0076908 -270.945 < 2e-16 ***
DESTIN_SZSGSZ06 0.4722873 0.0031764 148.688 < 2e-16 ***
DESTIN_SZSGSZ07 -0.3738603 0.0040739 -91.769 < 2e-16 ***
DESTIN_SZSISZ01 -1.0366212 0.0149155 -69.500 < 2e-16 ***
DESTIN_SZSKSZ01 0.0867897 0.0058855 14.746 < 2e-16 ***
DESTIN_SZSKSZ02 0.8624059 0.0041768 206.477 < 2e-16 ***
DESTIN_SZSKSZ03 0.1012121 0.0049653 20.384 < 2e-16 ***
DESTIN_SZSKSZ04 -0.5929946 0.0123979 -47.830 < 2e-16 ***
DESTIN_SZSKSZ05 0.1401700 0.0093658 14.966 < 2e-16 ***
DESTIN_SZSLSZ01 -0.3166943 0.0065782 -48.143 < 2e-16 ***
DESTIN_SZSLSZ04 -0.4358850 0.0054113 -80.551 < 2e-16 ***
DESTIN_SZSRSZ01 -1.7658362 0.0064403 -274.184 < 2e-16 ***
DESTIN_SZSRSZ02 -1.6963056 0.0074373 -228.080 < 2e-16 ***
DESTIN_SZSRSZ03 -1.6124371 0.0067798 -237.829 < 2e-16 ***
DESTIN_SZSVSZ01 -2.2156896 0.0269489 -82.218 < 2e-16 ***
DESTIN_SZTHSZ01 -2.8006440 0.0294349 -95.147 < 2e-16 ***
DESTIN_SZTHSZ03 -1.5367133 0.0167164 -91.928 < 2e-16 ***
DESTIN_SZTHSZ04 -2.2816064 0.0178897 -127.537 < 2e-16 ***
DESTIN_SZTHSZ06 -1.3482737 0.0115037 -117.203 < 2e-16 ***
DESTIN_SZTMSZ01 0.0774190 0.0042923 18.037 < 2e-16 ***
DESTIN_SZTMSZ02 1.7871993 0.0027927 639.959 < 2e-16 ***
DESTIN_SZTMSZ03 0.7024421 0.0032451 216.463 < 2e-16 ***
DESTIN_SZTMSZ04 0.7364739 0.0033642 218.914 < 2e-16 ***
DESTIN_SZTMSZ05 0.7048940 0.0040428 174.357 < 2e-16 ***
DESTIN_SZTNSZ01 -0.6225658 0.0044551 -139.742 < 2e-16 ***
DESTIN_SZTNSZ02 -1.5113237 0.0059073 -255.838 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4674552 0.0070568 -207.948 < 2e-16 ***
DESTIN_SZTNSZ04 -0.9951038 0.0054966 -181.041 < 2e-16 ***
DESTIN_SZTPSZ01 -0.6135726 0.0046111 -133.063 < 2e-16 ***
DESTIN_SZTPSZ02 0.2442119 0.0031727 76.973 < 2e-16 ***
DESTIN_SZTPSZ03 -0.5651733 0.0045904 -123.121 < 2e-16 ***
DESTIN_SZTPSZ04 -1.6056673 0.0062614 -256.441 < 2e-16 ***
DESTIN_SZTPSZ05 -0.9630062 0.0048582 -198.223 < 2e-16 ***
DESTIN_SZTPSZ06 -0.5977438 0.0054739 -109.199 < 2e-16 ***
DESTIN_SZTPSZ07 -1.8213815 0.0088310 -206.249 < 2e-16 ***
DESTIN_SZTPSZ08 -1.3162823 0.0064877 -202.889 < 2e-16 ***
DESTIN_SZTPSZ09 -0.6410718 0.0049764 -128.822 < 2e-16 ***
DESTIN_SZTPSZ10 -0.7050865 0.0059349 -118.803 < 2e-16 ***
DESTIN_SZTPSZ11 -0.3858008 0.0041409 -93.169 < 2e-16 ***
DESTIN_SZTPSZ12 -0.8578815 0.0051406 -166.884 < 2e-16 ***
DESTIN_SZTSSZ01 -0.7172064 0.0196905 -36.424 < 2e-16 ***
DESTIN_SZTSSZ02 1.1210809 0.0074311 150.864 < 2e-16 ***
DESTIN_SZTSSZ03 1.7457688 0.0055575 314.129 < 2e-16 ***
DESTIN_SZTSSZ04 1.6927966 0.0056353 300.394 < 2e-16 ***
DESTIN_SZTSSZ05 1.9380563 0.0058686 330.242 < 2e-16 ***
DESTIN_SZTSSZ06 0.9576149 0.0096946 98.778 < 2e-16 ***
DESTIN_SZWCSZ01 1.7027872 0.0037055 459.529 < 2e-16 ***
DESTIN_SZWCSZ02 -0.0626789 0.0081803 -7.662 1.83e-14 ***
DESTIN_SZWCSZ03 -1.1277080 0.0220290 -51.192 < 2e-16 ***
DESTIN_SZWDSZ01 1.7223563 0.0029499 583.867 < 2e-16 ***
DESTIN_SZWDSZ02 -0.3863906 0.0049400 -78.217 < 2e-16 ***
DESTIN_SZWDSZ03 1.2720234 0.0031005 410.261 < 2e-16 ***
DESTIN_SZWDSZ04 0.1720009 0.0044862 38.340 < 2e-16 ***
DESTIN_SZWDSZ05 0.1796788 0.0043625 41.187 < 2e-16 ***
DESTIN_SZWDSZ06 0.6674524 0.0034396 194.048 < 2e-16 ***
DESTIN_SZWDSZ07 0.4435607 0.0053544 82.841 < 2e-16 ***
DESTIN_SZWDSZ08 0.6200610 0.0051289 120.896 < 2e-16 ***
DESTIN_SZWDSZ09 0.8536490 0.0036814 231.879 < 2e-16 ***
DESTIN_SZYSSZ01 1.1556023 0.0031921 362.015 < 2e-16 ***
DESTIN_SZYSSZ02 0.1486836 0.0042025 35.380 < 2e-16 ***
DESTIN_SZYSSZ03 -0.1210199 0.0044490 -27.202 < 2e-16 ***
DESTIN_SZYSSZ04 -0.0262444 0.0041887 -6.266 3.72e-10 ***
DESTIN_SZYSSZ05 -1.5396810 0.0085529 -180.019 < 2e-16 ***
DESTIN_SZYSSZ06 -1.1632912 0.0066381 -175.246 < 2e-16 ***
DESTIN_SZYSSZ07 -0.8564919 0.0084362 -101.525 < 2e-16 ***
DESTIN_SZYSSZ08 0.8047469 0.0032867 244.853 < 2e-16 ***
DESTIN_SZYSSZ09 0.3870899 0.0034183 113.240 < 2e-16 ***
log(ORIGIN_AGE25_64) 0.2288630 0.0001068 2143.277 < 2e-16 ***
log(dist) -1.0087044 0.0001439 -7009.078 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 100298738 on 21188 degrees of freedom
Residual deviance: 36717627 on 20877 degrees of freedom
AIC: 36851578
Number of Fisher Scoring iterations: 7Lets check the R-square for this model.
# Compute R square of destination constrained SIM
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)[1] 0.53799It seems even better than the generalized linear regression this time.
16.4.5 Doubly constrained SIM
To calibrate a doubly constrained spatial interaction model (SIM), I will need to include both origin (ORIGIN_SZ) and destination (DESTIN_SZ).
The general formula of doubly constrained SIM is as follows:
\[ \lambda_{ij} = \exp(k + \mu_i + \alpha_i - \beta \ln d_{ij}) \]
# Calibrate doubly constrained SIM
dbcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
# Check output
summary(dbcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"),
data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 15.1999071 0.0038411 3957.125 < 2e-16 ***
ORIGIN_SZAMSZ02 0.9915322 0.0038375 258.380 < 2e-16 ***
ORIGIN_SZAMSZ03 0.5459405 0.0039401 138.561 < 2e-16 ***
ORIGIN_SZAMSZ04 0.1500977 0.0044098 34.037 < 2e-16 ***
ORIGIN_SZAMSZ05 0.0312761 0.0050308 6.217 5.07e-10 ***
ORIGIN_SZAMSZ06 0.4326936 0.0045672 94.738 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.7825778 0.0075844 -103.183 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.6243546 0.0071001 -87.937 < 2e-16 ***
ORIGIN_SZAMSZ09 0.3740520 0.0047038 79.521 < 2e-16 ***
ORIGIN_SZAMSZ10 0.2193746 0.0043532 50.394 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.5022103 0.0092960 -161.597 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.5341999 0.0092151 -166.487 < 2e-16 ***
ORIGIN_SZBDSZ01 0.6933547 0.0038949 178.018 < 2e-16 ***
ORIGIN_SZBDSZ02 0.3490622 0.0044578 78.304 < 2e-16 ***
ORIGIN_SZBDSZ03 0.7413352 0.0039623 187.099 < 2e-16 ***
ORIGIN_SZBDSZ04 1.3977900 0.0034993 399.450 < 2e-16 ***
ORIGIN_SZBDSZ05 0.5420249 0.0039506 137.200 < 2e-16 ***
ORIGIN_SZBDSZ06 0.8252248 0.0040223 205.164 < 2e-16 ***
ORIGIN_SZBDSZ07 -0.7602943 0.0071774 -105.929 < 2e-16 ***
ORIGIN_SZBDSZ08 -0.6345651 0.0069423 -91.406 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.0883137 0.0055472 -15.920 < 2e-16 ***
ORIGIN_SZBKSZ02 0.6137043 0.0045894 133.724 < 2e-16 ***
ORIGIN_SZBKSZ03 1.0261360 0.0042561 241.098 < 2e-16 ***
ORIGIN_SZBKSZ04 0.0290086 0.0051178 5.668 1.44e-08 ***
ORIGIN_SZBKSZ05 0.2606005 0.0047755 54.570 < 2e-16 ***
ORIGIN_SZBKSZ06 0.2777183 0.0051571 53.852 < 2e-16 ***
ORIGIN_SZBKSZ07 0.8621356 0.0039381 218.922 < 2e-16 ***
ORIGIN_SZBKSZ08 0.2931074 0.0045685 64.158 < 2e-16 ***
ORIGIN_SZBKSZ09 0.0664793 0.0048300 13.764 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.8396723 0.0110174 -166.979 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.9121521 0.0162227 -179.511 < 2e-16 ***
ORIGIN_SZBLSZ03 -4.9095995 0.0323514 -151.759 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.2019537 0.0158402 -139.011 < 2e-16 ***
ORIGIN_SZBMSZ01 0.2642502 0.0041728 63.327 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.0720760 0.0058485 -183.309 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.2168564 0.0047699 -45.463 < 2e-16 ***
ORIGIN_SZBMSZ04 0.1532123 0.0042484 36.063 < 2e-16 ***
ORIGIN_SZBMSZ05 -1.1312476 0.0063520 -178.093 < 2e-16 ***
ORIGIN_SZBMSZ06 -1.4253626 0.0096680 -147.431 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.3859298 0.0046971 -82.164 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.3021963 0.0047130 -64.120 < 2e-16 ***
ORIGIN_SZBMSZ09 -0.8447945 0.0059745 -141.399 < 2e-16 ***
ORIGIN_SZBMSZ10 -0.9654697 0.0063721 -151.515 < 2e-16 ***
ORIGIN_SZBMSZ11 -0.6449724 0.0055785 -115.618 < 2e-16 ***
ORIGIN_SZBMSZ12 -0.9045564 0.0071090 -127.241 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.0984943 0.0047108 -20.908 < 2e-16 ***
ORIGIN_SZBMSZ14 -0.3947883 0.0055640 -70.953 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.0670186 0.0050384 -13.301 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.0304019 0.0062676 -164.401 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.5214149 0.0095595 -159.151 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5918848 0.0048593 121.805 < 2e-16 ***
ORIGIN_SZBPSZ02 0.7502834 0.0053812 139.426 < 2e-16 ***
ORIGIN_SZBPSZ03 1.0497994 0.0050513 207.829 < 2e-16 ***
ORIGIN_SZBPSZ04 0.7998270 0.0043948 181.992 < 2e-16 ***
ORIGIN_SZBPSZ05 0.6344497 0.0040834 155.372 < 2e-16 ***
ORIGIN_SZBPSZ06 -0.7184362 0.0068817 -104.398 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.6410213 0.0068705 -93.300 < 2e-16 ***
ORIGIN_SZBSSZ01 0.0897803 0.0045857 19.578 < 2e-16 ***
ORIGIN_SZBSSZ02 0.5177060 0.0040884 126.627 < 2e-16 ***
ORIGIN_SZBSSZ03 0.1826677 0.0040716 44.864 < 2e-16 ***
ORIGIN_SZBTSZ01 0.1143941 0.0044839 25.512 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.7596921 0.0064272 -118.199 < 2e-16 ***
ORIGIN_SZBTSZ03 0.0078581 0.0047967 1.638 0.101376
ORIGIN_SZBTSZ04 -0.5542162 0.0078264 -70.814 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.3020091 0.0088150 -147.703 < 2e-16 ***
ORIGIN_SZBTSZ06 -0.5166223 0.0060186 -85.838 < 2e-16 ***
ORIGIN_SZBTSZ07 -1.4739046 0.0086314 -170.761 < 2e-16 ***
ORIGIN_SZBTSZ08 -0.8188637 0.0070822 -115.623 < 2e-16 ***
ORIGIN_SZCCSZ01 -1.4566001 0.0110387 -131.954 < 2e-16 ***
ORIGIN_SZCHSZ01 -1.1511546 0.0095567 -120.456 < 2e-16 ***
ORIGIN_SZCHSZ02 -1.0091323 0.0071330 -141.474 < 2e-16 ***
ORIGIN_SZCHSZ03 -0.6349303 0.0050675 -125.293 < 2e-16 ***
ORIGIN_SZCKSZ01 0.5862545 0.0043727 134.072 < 2e-16 ***
ORIGIN_SZCKSZ02 1.2397921 0.0044754 277.022 < 2e-16 ***
ORIGIN_SZCKSZ03 0.9544106 0.0040991 232.834 < 2e-16 ***
ORIGIN_SZCKSZ04 1.8476620 0.0042652 433.197 < 2e-16 ***
ORIGIN_SZCKSZ05 1.4217142 0.0051737 274.798 < 2e-16 ***
ORIGIN_SZCKSZ06 1.2099065 0.0054731 221.065 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.5769453 0.0059477 -97.003 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.3071187 0.0109631 -119.228 < 2e-16 ***
ORIGIN_SZCLSZ03 -0.2688092 0.0055806 -48.168 < 2e-16 ***
ORIGIN_SZCLSZ04 0.8057075 0.0039117 205.973 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.5032026 0.0103600 -145.097 < 2e-16 ***
ORIGIN_SZCLSZ06 0.8598831 0.0037475 229.452 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.0945484 0.0046487 -20.339 < 2e-16 ***
ORIGIN_SZCLSZ08 0.1685830 0.0052833 31.909 < 2e-16 ***
ORIGIN_SZCLSZ09 -2.0782601 0.0133652 -155.497 < 2e-16 ***
ORIGIN_SZDTSZ01 -1.5177479 0.0071825 -211.313 < 2e-16 ***
ORIGIN_SZDTSZ02 -1.4412957 0.0067816 -212.531 < 2e-16 ***
ORIGIN_SZDTSZ03 -2.8232111 0.0149809 -188.454 < 2e-16 ***
ORIGIN_SZDTSZ04 -4.5473293 0.0831203 -54.708 < 2e-16 ***
ORIGIN_SZDTSZ05 -3.1955067 0.0243445 -131.262 < 2e-16 ***
ORIGIN_SZDTSZ06 -3.0968326 0.0194144 -159.512 < 2e-16 ***
ORIGIN_SZDTSZ07 -1.7961514 0.0190194 -94.438 < 2e-16 ***
ORIGIN_SZDTSZ08 -2.1578198 0.0098435 -219.213 < 2e-16 ***
ORIGIN_SZDTSZ09 -2.9845675 0.0209502 -142.460 < 2e-16 ***
ORIGIN_SZDTSZ10 -1.9507307 0.0105356 -185.156 < 2e-16 ***
ORIGIN_SZDTSZ11 -2.1186970 0.0109398 -193.669 < 2e-16 ***
ORIGIN_SZDTSZ12 -3.3084532 0.0270350 -122.377 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.1198093 0.0126303 -167.836 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.4640769 0.0073543 -199.077 < 2e-16 ***
ORIGIN_SZGLSZ02 0.1870597 0.0042616 43.894 < 2e-16 ***
ORIGIN_SZGLSZ03 0.0024448 0.0042456 0.576 0.564716
ORIGIN_SZGLSZ04 0.9755121 0.0036050 270.600 < 2e-16 ***
ORIGIN_SZGLSZ05 0.5916150 0.0038113 155.228 < 2e-16 ***
ORIGIN_SZHGSZ01 0.1415108 0.0041985 33.705 < 2e-16 ***
ORIGIN_SZHGSZ02 0.6532600 0.0040314 162.043 < 2e-16 ***
ORIGIN_SZHGSZ03 0.4005506 0.0044027 90.978 < 2e-16 ***
ORIGIN_SZHGSZ04 0.9410951 0.0037639 250.032 < 2e-16 ***
ORIGIN_SZHGSZ05 1.2614729 0.0037176 339.322 < 2e-16 ***
ORIGIN_SZHGSZ06 0.1839934 0.0044258 41.573 < 2e-16 ***
ORIGIN_SZHGSZ07 0.5969164 0.0038971 153.171 < 2e-16 ***
ORIGIN_SZHGSZ08 0.1126282 0.0044590 25.259 < 2e-16 ***
ORIGIN_SZHGSZ09 -0.8628496 0.0061992 -139.188 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.3887988 0.0386181 -87.752 < 2e-16 ***
ORIGIN_SZJESZ01 0.5275335 0.0044054 119.746 < 2e-16 ***
ORIGIN_SZJESZ02 0.3608775 0.0043963 82.087 < 2e-16 ***
ORIGIN_SZJESZ03 0.2981338 0.0046180 64.559 < 2e-16 ***
ORIGIN_SZJESZ04 -0.9640666 0.0071627 -134.596 < 2e-16 ***
ORIGIN_SZJESZ05 -2.0025807 0.0121405 -164.950 < 2e-16 ***
ORIGIN_SZJESZ06 0.2914311 0.0042418 68.705 < 2e-16 ***
ORIGIN_SZJESZ07 -1.6629057 0.0092689 -179.407 < 2e-16 ***
ORIGIN_SZJESZ08 -0.7484714 0.0086390 -86.638 < 2e-16 ***
ORIGIN_SZJESZ09 0.4110434 0.0045994 89.368 < 2e-16 ***
ORIGIN_SZJESZ10 -2.7575422 0.0172464 -159.891 < 2e-16 ***
ORIGIN_SZJESZ11 -2.9663269 0.0163303 -181.646 < 2e-16 ***
ORIGIN_SZJWSZ01 0.4687678 0.0059492 78.795 < 2e-16 ***
ORIGIN_SZJWSZ02 0.9705535 0.0041073 236.298 < 2e-16 ***
ORIGIN_SZJWSZ03 1.2316748 0.0039038 315.509 < 2e-16 ***
ORIGIN_SZJWSZ04 0.9397664 0.0040281 233.302 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.6480856 0.0104785 -157.283 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.2429625 0.0089470 -138.924 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.2886752 0.0217756 -105.103 < 2e-16 ***
ORIGIN_SZJWSZ08 1.9572281 0.0039391 496.878 < 2e-16 ***
ORIGIN_SZJWSZ09 1.5497800 0.0036573 423.751 < 2e-16 ***
ORIGIN_SZKLSZ01 0.3028599 0.0040853 74.133 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.3592514 0.0050640 -70.943 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.3665571 0.0050790 -72.171 < 2e-16 ***
ORIGIN_SZKLSZ04 -1.3306775 0.0070493 -188.768 < 2e-16 ***
ORIGIN_SZKLSZ05 -0.6377843 0.0068139 -93.600 < 2e-16 ***
ORIGIN_SZKLSZ06 -0.3764310 0.0047419 -79.383 < 2e-16 ***
ORIGIN_SZKLSZ07 -0.8171896 0.0062230 -131.317 < 2e-16 ***
ORIGIN_SZKLSZ08 -0.7576831 0.0054082 -140.099 < 2e-16 ***
ORIGIN_SZKLSZ09 -1.2766253 0.0068207 -187.170 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.4416684 0.0322208 -75.779 < 2e-16 ***
ORIGIN_SZMDSZ01 -1.4298089 0.0230585 -62.008 < 2e-16 ***
ORIGIN_SZMDSZ02 -1.0512485 0.0103599 -101.473 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.3650799 0.0136453 -100.041 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.8222832 0.0066772 -123.148 < 2e-16 ***
ORIGIN_SZMPSZ02 -0.4930735 0.0055822 -88.330 < 2e-16 ***
ORIGIN_SZMPSZ03 0.1206676 0.0044729 26.977 < 2e-16 ***
ORIGIN_SZMSSZ01 -6.1448907 0.3783240 -16.242 < 2e-16 ***
ORIGIN_SZMUSZ01 -1.0357465 0.0059323 -174.593 < 2e-16 ***
ORIGIN_SZMUSZ02 -2.8753850 0.0145064 -198.215 < 2e-16 ***
ORIGIN_SZMUSZ03 -1.6027106 0.0069588 -230.314 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.3258427 0.0249185 -93.338 < 2e-16 ***
ORIGIN_SZNTSZ02 -2.2356147 0.0130994 -170.666 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.6006927 0.0060806 -98.788 < 2e-16 ***
ORIGIN_SZNTSZ05 -2.7454600 0.0381994 -71.872 < 2e-16 ***
ORIGIN_SZNTSZ06 -2.8527612 0.0380950 -74.885 < 2e-16 ***
ORIGIN_SZNVSZ01 0.7867941 0.0037384 210.462 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.3211425 0.0049912 -64.342 < 2e-16 ***
ORIGIN_SZNVSZ03 -0.9846200 0.0062096 -158.563 < 2e-16 ***
ORIGIN_SZNVSZ04 -1.0429028 0.0072490 -143.868 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.2875679 0.0134296 -170.337 < 2e-16 ***
ORIGIN_SZORSZ01 -3.0093493 0.0283014 -106.332 < 2e-16 ***
ORIGIN_SZORSZ02 -1.0826302 0.0059205 -182.861 < 2e-16 ***
ORIGIN_SZORSZ03 -1.4430368 0.0069826 -206.661 < 2e-16 ***
ORIGIN_SZOTSZ01 -1.4138143 0.0073317 -192.835 < 2e-16 ***
ORIGIN_SZOTSZ02 -1.5832107 0.0083193 -190.307 < 2e-16 ***
ORIGIN_SZOTSZ03 -0.6817735 0.0055117 -123.697 < 2e-16 ***
ORIGIN_SZOTSZ04 -0.5769425 0.0084627 -68.175 < 2e-16 ***
ORIGIN_SZPGSZ01 0.4918602 0.0106117 46.351 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.2535855 0.0060460 -41.943 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9676637 0.0039062 247.725 < 2e-16 ***
ORIGIN_SZPGSZ04 1.2021981 0.0038906 308.998 < 2e-16 ***
ORIGIN_SZPGSZ05 0.6313102 0.0048367 130.526 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.7008879 0.0082199 -85.267 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0392767 0.0114120 -91.069 < 2e-16 ***
ORIGIN_SZPLSZ03 -3.1460244 0.0299993 -104.870 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.4808985 0.0311916 -111.597 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.2810839 0.0181023 -126.011 < 2e-16 ***
ORIGIN_SZPNSZ01 0.8973191 0.0048920 183.425 < 2e-16 ***
ORIGIN_SZPNSZ02 -1.7900570 0.0113564 -157.625 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.6608189 0.0175462 -151.646 < 2e-16 ***
ORIGIN_SZPNSZ04 -4.6380282 0.0258895 -179.147 < 2e-16 ***
ORIGIN_SZPNSZ05 -3.2786556 0.0202668 -161.775 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.8037609 0.0099114 -81.095 < 2e-16 ***
ORIGIN_SZPRSZ02 0.9923745 0.0040751 243.524 < 2e-16 ***
ORIGIN_SZPRSZ03 0.4383760 0.0040685 107.750 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.5009913 0.0065068 -76.995 < 2e-16 ***
ORIGIN_SZPRSZ05 1.0651605 0.0038956 273.428 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.0037905 0.0070414 -142.555 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.6545509 0.0167423 -158.554 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.0713911 0.0052880 -13.500 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.0630253 0.0056532 -11.149 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.4527135 0.0051869 -87.281 < 2e-16 ***
ORIGIN_SZQTSZ03 0.0386662 0.0049026 7.887 3.10e-15 ***
ORIGIN_SZQTSZ04 -0.9527320 0.0061671 -154.486 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.0318211 0.0048272 -6.592 4.34e-11 ***
ORIGIN_SZQTSZ06 -0.2858340 0.0054044 -52.889 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.2914572 0.0079902 -161.629 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.2915213 0.0049117 -59.353 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.5801288 0.0057174 -101.467 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.4703719 0.0054963 -85.579 < 2e-16 ***
ORIGIN_SZQTSZ11 -1.5005437 0.0076206 -196.905 < 2e-16 ***
ORIGIN_SZQTSZ12 -0.7578962 0.0065876 -115.049 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.2490102 0.0051259 -48.579 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.3967186 0.0072948 -191.467 < 2e-16 ***
ORIGIN_SZQTSZ15 -1.1921101 0.0088686 -134.419 < 2e-16 ***
ORIGIN_SZRCSZ01 -0.4780365 0.0054343 -87.967 < 2e-16 ***
ORIGIN_SZRCSZ02 -2.1522223 0.0157715 -136.463 < 2e-16 ***
ORIGIN_SZRCSZ03 -1.1376830 0.0075137 -151.414 < 2e-16 ***
ORIGIN_SZRCSZ04 -2.0998523 0.0111226 -188.792 < 2e-16 ***
ORIGIN_SZRCSZ05 -2.4737348 0.0137552 -179.840 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.1484671 0.0072307 -20.533 < 2e-16 ***
ORIGIN_SZRCSZ08 -2.2917415 0.0162442 -141.081 < 2e-16 ***
ORIGIN_SZRCSZ09 -1.7531756 0.0124619 -140.683 < 2e-16 ***
ORIGIN_SZRCSZ10 -1.5786376 0.0070864 -222.772 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.4898986 0.0129726 -191.935 < 2e-16 ***
ORIGIN_SZRVSZ02 -0.8417995 0.0068297 -123.256 < 2e-16 ***
ORIGIN_SZRVSZ03 -1.4346434 0.0097511 -147.126 < 2e-16 ***
ORIGIN_SZRVSZ04 -1.7082240 0.0139212 -122.707 < 2e-16 ***
ORIGIN_SZRVSZ05 -1.7513661 0.0121335 -144.342 < 2e-16 ***
ORIGIN_SZSBSZ01 0.9754567 0.0049247 198.074 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.5628799 0.0066575 -84.549 < 2e-16 ***
ORIGIN_SZSBSZ03 0.6616685 0.0042705 154.938 < 2e-16 ***
ORIGIN_SZSBSZ04 0.4253573 0.0049524 85.889 < 2e-16 ***
ORIGIN_SZSBSZ05 0.0103021 0.0058324 1.766 0.077334 .
ORIGIN_SZSBSZ06 -0.9730293 0.0143338 -67.884 < 2e-16 ***
ORIGIN_SZSBSZ07 0.0366673 0.0098280 3.731 0.000191 ***
ORIGIN_SZSBSZ08 -1.9716652 0.0099961 -197.244 < 2e-16 ***
ORIGIN_SZSBSZ09 -1.0257192 0.0074185 -138.266 < 2e-16 ***
ORIGIN_SZSESZ02 1.2003983 0.0038187 314.346 < 2e-16 ***
ORIGIN_SZSESZ03 1.1116771 0.0036759 302.424 < 2e-16 ***
ORIGIN_SZSESZ04 1.0576059 0.0042091 251.266 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2013289 0.0050541 -39.835 < 2e-16 ***
ORIGIN_SZSESZ06 1.1326368 0.0039889 283.950 < 2e-16 ***
ORIGIN_SZSESZ07 -1.8619033 0.0141423 -131.655 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.8265775 0.0072006 -114.792 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.2855959 0.0083996 -153.055 < 2e-16 ***
ORIGIN_SZSGSZ03 0.2726552 0.0044852 60.790 < 2e-16 ***
ORIGIN_SZSGSZ04 0.4106394 0.0040894 100.415 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.5830761 0.0085928 -184.233 < 2e-16 ***
ORIGIN_SZSGSZ06 0.3447324 0.0039288 87.745 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.5230863 0.0051521 -101.529 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.0708352 0.0070461 -10.053 < 2e-16 ***
ORIGIN_SZSKSZ02 0.2663741 0.0053515 49.776 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.3245853 0.0064849 -50.052 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.9682010 0.0226854 -86.761 < 2e-16 ***
ORIGIN_SZSKSZ05 -1.2037861 0.0141172 -85.271 < 2e-16 ***
ORIGIN_SZSLSZ01 -3.0067731 0.0268121 -112.142 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.2408349 0.0060503 -39.805 < 2e-16 ***
ORIGIN_SZSRSZ01 -1.2025265 0.0072145 -166.682 < 2e-16 ***
ORIGIN_SZSRSZ02 -1.4810758 0.0073378 -201.842 < 2e-16 ***
ORIGIN_SZSRSZ03 -2.4986726 0.0150646 -165.864 < 2e-16 ***
ORIGIN_SZSVSZ01 -2.4468090 0.0356146 -68.703 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.6433817 0.0452493 -58.418 < 2e-16 ***
ORIGIN_SZTHSZ03 -0.9313859 0.0129174 -72.103 < 2e-16 ***
ORIGIN_SZTHSZ04 -1.9528220 0.0240275 -81.275 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.1556098 0.0108689 -106.322 < 2e-16 ***
ORIGIN_SZTMSZ01 0.6084055 0.0044135 137.852 < 2e-16 ***
ORIGIN_SZTMSZ02 1.5436121 0.0034453 448.031 < 2e-16 ***
ORIGIN_SZTMSZ03 1.1852360 0.0036421 325.425 < 2e-16 ***
ORIGIN_SZTMSZ04 0.3951167 0.0042346 93.308 < 2e-16 ***
ORIGIN_SZTMSZ05 -0.9556999 0.0066658 -143.373 < 2e-16 ***
ORIGIN_SZTNSZ01 -0.8834358 0.0062125 -142.202 < 2e-16 ***
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ORIGIN_SZTPSZ01 -0.5010324 0.0053698 -93.305 < 2e-16 ***
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ORIGIN_SZTPSZ03 -0.5180138 0.0053842 -96.210 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.2086734 0.0050049 -41.693 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.1074656 0.0051891 -20.710 < 2e-16 ***
ORIGIN_SZTPSZ06 0.4586729 0.0055576 82.530 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.1199714 0.0052051 -23.049 < 2e-16 ***
ORIGIN_SZTPSZ08 -0.5074852 0.0068250 -74.357 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.5392473 0.0055201 -97.689 < 2e-16 ***
ORIGIN_SZTPSZ10 -0.3111562 0.0056043 -55.521 < 2e-16 ***
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ORIGIN_SZTSSZ01 -3.2942604 0.0410073 -80.333 < 2e-16 ***
ORIGIN_SZTSSZ02 0.0886812 0.0080703 10.989 < 2e-16 ***
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ORIGIN_SZTSSZ04 -0.7144742 0.0084663 -84.390 < 2e-16 ***
ORIGIN_SZTSSZ05 -2.8037139 0.0131321 -213.501 < 2e-16 ***
ORIGIN_SZTSSZ06 -3.3945573 0.0193276 -175.632 < 2e-16 ***
ORIGIN_SZWCSZ01 -0.8678171 0.0065959 -131.568 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.6973891 0.0256373 -105.213 < 2e-16 ***
ORIGIN_SZWCSZ03 -4.6115565 0.1187370 -38.838 < 2e-16 ***
ORIGIN_SZWDSZ01 0.9038540 0.0038107 237.187 < 2e-16 ***
ORIGIN_SZWDSZ02 0.9422172 0.0042893 219.668 < 2e-16 ***
ORIGIN_SZWDSZ03 1.6903891 0.0038831 435.324 < 2e-16 ***
ORIGIN_SZWDSZ04 1.1333527 0.0046724 242.564 < 2e-16 ***
ORIGIN_SZWDSZ05 0.5945016 0.0045045 131.980 < 2e-16 ***
ORIGIN_SZWDSZ06 0.9826771 0.0042416 231.675 < 2e-16 ***
ORIGIN_SZWDSZ07 -0.1575232 0.0061736 -25.516 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.7931466 0.0069921 -113.435 < 2e-16 ***
ORIGIN_SZWDSZ09 1.6716643 0.0040142 416.442 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.4093427 0.0049649 -82.447 < 2e-16 ***
ORIGIN_SZYSSZ02 0.9221490 0.0046156 199.790 < 2e-16 ***
ORIGIN_SZYSSZ03 2.0586447 0.0038523 534.397 < 2e-16 ***
ORIGIN_SZYSSZ04 0.9294138 0.0039757 233.775 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4557284 0.0047843 95.254 < 2e-16 ***
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ORIGIN_SZYSSZ07 -0.4572689 0.0082899 -55.160 < 2e-16 ***
ORIGIN_SZYSSZ08 -0.4737067 0.0055040 -86.067 < 2e-16 ***
ORIGIN_SZYSSZ09 1.1781077 0.0038895 302.893 < 2e-16 ***
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DESTIN_SZAMSZ04 -0.9991004 0.0053586 -186.448 < 2e-16 ***
DESTIN_SZAMSZ05 -0.8848530 0.0051151 -172.989 < 2e-16 ***
DESTIN_SZAMSZ06 -0.7481102 0.0049376 -151.513 < 2e-16 ***
DESTIN_SZAMSZ07 -1.6646236 0.0087835 -189.517 < 2e-16 ***
DESTIN_SZAMSZ08 -0.7232492 0.0055230 -130.952 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0122575 0.0053562 -188.988 < 2e-16 ***
DESTIN_SZAMSZ10 0.1537791 0.0036945 41.624 < 2e-16 ***
DESTIN_SZAMSZ11 -0.0447198 0.0062129 -7.198 6.12e-13 ***
DESTIN_SZAMSZ12 -0.6421683 0.0058839 -109.140 < 2e-16 ***
DESTIN_SZBDSZ01 0.5058493 0.0034094 148.367 < 2e-16 ***
DESTIN_SZBDSZ02 -0.2717119 0.0043145 -62.976 < 2e-16 ***
DESTIN_SZBDSZ03 -0.0120332 0.0038108 -3.158 0.001590 **
DESTIN_SZBDSZ04 0.7803347 0.0031666 246.427 < 2e-16 ***
DESTIN_SZBDSZ05 0.5173032 0.0034863 148.384 < 2e-16 ***
DESTIN_SZBDSZ06 0.0154145 0.0039635 3.889 0.000101 ***
DESTIN_SZBDSZ07 -0.6918517 0.0078904 -87.682 < 2e-16 ***
DESTIN_SZBDSZ08 -1.2918718 0.0075749 -170.547 < 2e-16 ***
DESTIN_SZBKSZ01 -1.3974144 0.0057919 -241.269 < 2e-16 ***
DESTIN_SZBKSZ02 -0.5518467 0.0047951 -115.086 < 2e-16 ***
DESTIN_SZBKSZ03 -0.8529731 0.0047189 -180.758 < 2e-16 ***
DESTIN_SZBKSZ04 -0.2714960 0.0042971 -63.181 < 2e-16 ***
DESTIN_SZBKSZ05 -0.6157950 0.0047352 -130.047 < 2e-16 ***
DESTIN_SZBKSZ06 -1.0440527 0.0052560 -198.640 < 2e-16 ***
DESTIN_SZBKSZ07 0.0065723 0.0036945 1.779 0.075253 .
DESTIN_SZBKSZ08 -1.1893742 0.0059193 -200.932 < 2e-16 ***
DESTIN_SZBKSZ09 -0.2163686 0.0043209 -50.075 < 2e-16 ***
DESTIN_SZBLSZ01 -0.7414429 0.0061120 -121.310 < 2e-16 ***
DESTIN_SZBLSZ02 0.3444230 0.0058769 58.606 < 2e-16 ***
DESTIN_SZBLSZ03 1.6121676 0.0063877 252.387 < 2e-16 ***
DESTIN_SZBLSZ04 -0.5006334 0.0118243 -42.339 < 2e-16 ***
DESTIN_SZBMSZ01 0.1389169 0.0039066 35.559 < 2e-16 ***
DESTIN_SZBMSZ02 -0.0952267 0.0040569 -23.473 < 2e-16 ***
DESTIN_SZBMSZ03 -0.5152067 0.0049850 -103.352 < 2e-16 ***
DESTIN_SZBMSZ04 -0.2622231 0.0043201 -60.698 < 2e-16 ***
DESTIN_SZBMSZ05 -0.2947874 0.0050816 -58.010 < 2e-16 ***
DESTIN_SZBMSZ06 -1.1956385 0.0087573 -136.531 < 2e-16 ***
DESTIN_SZBMSZ07 0.2620893 0.0038243 68.532 < 2e-16 ***
DESTIN_SZBMSZ08 -0.7233463 0.0049997 -144.678 < 2e-16 ***
DESTIN_SZBMSZ09 -1.4801415 0.0076791 -192.750 < 2e-16 ***
DESTIN_SZBMSZ10 -1.0568332 0.0061534 -171.749 < 2e-16 ***
DESTIN_SZBMSZ11 -1.1755381 0.0061881 -189.967 < 2e-16 ***
DESTIN_SZBMSZ12 -0.4756214 0.0061485 -77.356 < 2e-16 ***
DESTIN_SZBMSZ13 0.1640918 0.0040753 40.265 < 2e-16 ***
DESTIN_SZBMSZ14 -0.7245876 0.0064607 -112.153 < 2e-16 ***
DESTIN_SZBMSZ15 -0.9374745 0.0061199 -153.186 < 2e-16 ***
DESTIN_SZBMSZ16 -1.1297224 0.0062235 -181.526 < 2e-16 ***
DESTIN_SZBMSZ17 -1.1496478 0.0073709 -155.971 < 2e-16 ***
DESTIN_SZBPSZ01 -0.9160863 0.0047624 -192.358 < 2e-16 ***
DESTIN_SZBPSZ02 -1.9731256 0.0078054 -252.788 < 2e-16 ***
DESTIN_SZBPSZ03 -1.7606427 0.0072516 -242.792 < 2e-16 ***
DESTIN_SZBPSZ04 -0.9986932 0.0052769 -189.257 < 2e-16 ***
DESTIN_SZBPSZ05 0.2720045 0.0035451 76.726 < 2e-16 ***
DESTIN_SZBPSZ06 -0.8102457 0.0063352 -127.897 < 2e-16 ***
DESTIN_SZBPSZ07 -0.5438293 0.0065632 -82.861 < 2e-16 ***
DESTIN_SZBSSZ01 0.0658141 0.0039354 16.723 < 2e-16 ***
DESTIN_SZBSSZ02 -0.7261582 0.0045059 -161.156 < 2e-16 ***
DESTIN_SZBSSZ03 0.4168651 0.0033193 125.588 < 2e-16 ***
DESTIN_SZBTSZ01 0.2721995 0.0036873 73.822 < 2e-16 ***
DESTIN_SZBTSZ02 -0.5251752 0.0055795 -94.126 < 2e-16 ***
DESTIN_SZBTSZ03 -0.0069795 0.0043750 -1.595 0.110645
DESTIN_SZBTSZ04 -1.0844470 0.0083834 -129.357 < 2e-16 ***
DESTIN_SZBTSZ05 -0.3760852 0.0060799 -61.857 < 2e-16 ***
DESTIN_SZBTSZ06 -0.5516357 0.0053702 -102.721 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4446318 0.0079566 -181.565 < 2e-16 ***
DESTIN_SZBTSZ08 -0.7546447 0.0070907 -106.427 < 2e-16 ***
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DESTIN_SZCKSZ04 -1.6245356 0.0056977 -285.123 < 2e-16 ***
DESTIN_SZCKSZ05 -1.3649438 0.0064202 -212.603 < 2e-16 ***
DESTIN_SZCKSZ06 -0.0280029 0.0051149 -5.475 4.38e-08 ***
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DESTIN_SZCLSZ03 -0.8871207 0.0063921 -138.783 < 2e-16 ***
DESTIN_SZCLSZ04 -0.0131578 0.0038729 -3.397 0.000680 ***
DESTIN_SZCLSZ05 -0.9641034 0.0071434 -134.964 < 2e-16 ***
DESTIN_SZCLSZ06 0.1421506 0.0036260 39.203 < 2e-16 ***
DESTIN_SZCLSZ07 -0.4423813 0.0045961 -96.252 < 2e-16 ***
DESTIN_SZCLSZ08 -0.3693630 0.0052645 -70.161 < 2e-16 ***
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DESTIN_SZDTSZ02 -0.5704531 0.0044652 -127.755 < 2e-16 ***
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DESTIN_SZDTSZ06 -1.0365903 0.0063734 -162.644 < 2e-16 ***
DESTIN_SZDTSZ07 -1.8499276 0.0184530 -100.251 < 2e-16 ***
DESTIN_SZDTSZ08 -0.2969690 0.0043333 -68.531 < 2e-16 ***
DESTIN_SZDTSZ09 -1.2998740 0.0092852 -139.994 < 2e-16 ***
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DESTIN_SZDTSZ12 -2.1185871 0.0148380 -142.782 < 2e-16 ***
DESTIN_SZDTSZ13 -1.6194904 0.0095412 -169.736 < 2e-16 ***
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DESTIN_SZGLSZ03 0.5049337 0.0033917 148.875 < 2e-16 ***
DESTIN_SZGLSZ04 0.4368105 0.0033449 130.591 < 2e-16 ***
DESTIN_SZGLSZ05 0.2343129 0.0035076 66.801 < 2e-16 ***
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DESTIN_SZJWSZ02 -0.8963200 0.0048611 -184.387 < 2e-16 ***
DESTIN_SZJWSZ03 0.0993342 0.0038224 25.988 < 2e-16 ***
DESTIN_SZJWSZ04 0.6387926 0.0035927 177.801 < 2e-16 ***
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DESTIN_SZJWSZ06 -0.3465058 0.0049105 -70.564 < 2e-16 ***
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DESTIN_SZJWSZ08 -0.6874421 0.0044423 -154.750 < 2e-16 ***
DESTIN_SZJWSZ09 0.8189854 0.0032936 248.658 < 2e-16 ***
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DESTIN_SZPNSZ03 -0.0131647 0.0068564 -1.920 0.054852 .
DESTIN_SZPNSZ04 1.7753521 0.0075477 235.217 < 2e-16 ***
DESTIN_SZPNSZ05 1.1056489 0.0108712 101.704 < 2e-16 ***
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DESTIN_SZQTSZ13 0.3625297 0.0042169 85.971 < 2e-16 ***
DESTIN_SZQTSZ14 0.3304396 0.0045989 71.851 < 2e-16 ***
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DESTIN_SZRCSZ09 -1.1812502 0.0094701 -124.734 < 2e-16 ***
DESTIN_SZRCSZ10 -0.6089679 0.0051111 -119.146 < 2e-16 ***
DESTIN_SZRVSZ01 -1.5976715 0.0088190 -181.163 < 2e-16 ***
DESTIN_SZRVSZ02 -2.1525165 0.0119212 -180.562 < 2e-16 ***
DESTIN_SZRVSZ03 -1.9507131 0.0104298 -187.032 < 2e-16 ***
DESTIN_SZRVSZ04 -1.4037579 0.0118697 -118.264 < 2e-16 ***
DESTIN_SZRVSZ05 -1.4229374 0.0112906 -126.028 < 2e-16 ***
DESTIN_SZSBSZ01 -0.6277159 0.0052328 -119.959 < 2e-16 ***
DESTIN_SZSBSZ02 -1.1412070 0.0061425 -185.787 < 2e-16 ***
DESTIN_SZSBSZ03 0.3589648 0.0038681 92.801 < 2e-16 ***
DESTIN_SZSBSZ04 -0.0709076 0.0050492 -14.043 < 2e-16 ***
DESTIN_SZSBSZ05 -1.0427480 0.0060587 -172.109 < 2e-16 ***
DESTIN_SZSBSZ06 -2.3444927 0.0228529 -102.591 < 2e-16 ***
DESTIN_SZSBSZ07 -2.1716360 0.0168611 -128.795 < 2e-16 ***
DESTIN_SZSBSZ08 0.9940071 0.0045960 216.279 < 2e-16 ***
DESTIN_SZSBSZ09 0.3853085 0.0045130 85.377 < 2e-16 ***
DESTIN_SZSESZ02 -0.5774019 0.0041260 -139.942 < 2e-16 ***
DESTIN_SZSESZ03 0.3705298 0.0032705 113.293 < 2e-16 ***
DESTIN_SZSESZ04 -0.8818473 0.0047175 -186.931 < 2e-16 ***
DESTIN_SZSESZ05 -0.2972465 0.0039562 -75.134 < 2e-16 ***
DESTIN_SZSESZ06 -0.8698024 0.0049988 -174.001 < 2e-16 ***
DESTIN_SZSESZ07 -3.1274891 0.0193622 -161.526 < 2e-16 ***
DESTIN_SZSGSZ01 -0.1963321 0.0049786 -39.435 < 2e-16 ***
DESTIN_SZSGSZ02 -0.1700883 0.0043459 -39.138 < 2e-16 ***
DESTIN_SZSGSZ03 -0.4524480 0.0041809 -108.218 < 2e-16 ***
DESTIN_SZSGSZ04 -0.2295840 0.0040411 -56.812 < 2e-16 ***
DESTIN_SZSGSZ05 -1.8766540 0.0077291 -242.802 < 2e-16 ***
DESTIN_SZSGSZ06 0.4732513 0.0032728 144.602 < 2e-16 ***
DESTIN_SZSGSZ07 -0.3157314 0.0041621 -75.859 < 2e-16 ***
DESTIN_SZSISZ01 -0.5455678 0.0150088 -36.350 < 2e-16 ***
DESTIN_SZSKSZ01 -0.6771439 0.0063703 -106.297 < 2e-16 ***
DESTIN_SZSKSZ02 0.2254683 0.0047529 47.438 < 2e-16 ***
DESTIN_SZSKSZ03 -0.4962535 0.0052887 -93.832 < 2e-16 ***
DESTIN_SZSKSZ04 -0.9962895 0.0132331 -75.288 < 2e-16 ***
DESTIN_SZSKSZ05 -0.4727211 0.0108675 -43.499 < 2e-16 ***
DESTIN_SZSLSZ01 -0.6844518 0.0066958 -102.221 < 2e-16 ***
DESTIN_SZSLSZ04 -0.8642566 0.0055529 -155.640 < 2e-16 ***
DESTIN_SZSRSZ01 -1.1258378 0.0065445 -172.028 < 2e-16 ***
DESTIN_SZSRSZ02 -1.2210342 0.0075209 -162.353 < 2e-16 ***
DESTIN_SZSRSZ03 -1.3916299 0.0068324 -203.679 < 2e-16 ***
DESTIN_SZSVSZ01 -0.8502501 0.0357682 -23.771 < 2e-16 ***
DESTIN_SZTHSZ01 -3.6862493 0.0295142 -124.897 < 2e-16 ***
DESTIN_SZTHSZ03 -2.1656897 0.0172029 -125.891 < 2e-16 ***
DESTIN_SZTHSZ04 -2.6708338 0.0180519 -147.953 < 2e-16 ***
DESTIN_SZTHSZ06 -1.8096992 0.0117190 -154.424 < 2e-16 ***
DESTIN_SZTMSZ01 -0.2650161 0.0045695 -57.996 < 2e-16 ***
DESTIN_SZTMSZ02 1.3613330 0.0030137 451.713 < 2e-16 ***
DESTIN_SZTMSZ03 0.4088507 0.0034676 117.906 < 2e-16 ***
DESTIN_SZTMSZ04 0.6607530 0.0036103 183.019 < 2e-16 ***
DESTIN_SZTMSZ05 0.7477414 0.0043234 172.950 < 2e-16 ***
DESTIN_SZTNSZ01 -0.2329343 0.0045763 -50.900 < 2e-16 ***
DESTIN_SZTNSZ02 -0.9645287 0.0060146 -160.364 < 2e-16 ***
DESTIN_SZTNSZ03 -0.9866474 0.0071782 -137.450 < 2e-16 ***
DESTIN_SZTNSZ04 -0.7708811 0.0056325 -136.862 < 2e-16 ***
DESTIN_SZTPSZ01 -0.3571909 0.0047134 -75.782 < 2e-16 ***
DESTIN_SZTPSZ02 0.3556574 0.0032813 108.388 < 2e-16 ***
DESTIN_SZTPSZ03 -0.2721489 0.0047418 -57.394 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5204272 0.0063397 -239.826 < 2e-16 ***
DESTIN_SZTPSZ05 -0.9207192 0.0049711 -185.215 < 2e-16 ***
DESTIN_SZTPSZ06 -0.5985909 0.0060527 -98.897 < 2e-16 ***
DESTIN_SZTPSZ07 -1.7525701 0.0089843 -195.071 < 2e-16 ***
DESTIN_SZTPSZ08 -1.1401529 0.0066203 -172.221 < 2e-16 ***
DESTIN_SZTPSZ09 -0.3502863 0.0051273 -68.318 < 2e-16 ***
DESTIN_SZTPSZ10 -0.8499288 0.0060719 -139.978 < 2e-16 ***
DESTIN_SZTPSZ11 -0.2549491 0.0042766 -59.615 < 2e-16 ***
DESTIN_SZTPSZ12 -0.6839606 0.0052451 -130.399 < 2e-16 ***
DESTIN_SZTSSZ01 -1.2535386 0.0205589 -60.973 < 2e-16 ***
DESTIN_SZTSSZ02 -0.5129383 0.0096015 -53.423 < 2e-16 ***
DESTIN_SZTSSZ03 0.3123557 0.0076756 40.695 < 2e-16 ***
DESTIN_SZTSSZ04 0.6030653 0.0076016 79.334 < 2e-16 ***
DESTIN_SZTSSZ05 1.6523766 0.0077730 212.580 < 2e-16 ***
DESTIN_SZTSSZ06 1.8829996 0.0142804 131.859 < 2e-16 ***
DESTIN_SZWCSZ01 1.3448747 0.0043570 308.670 < 2e-16 ***
DESTIN_SZWCSZ02 -1.0146962 0.0084952 -119.443 < 2e-16 ***
DESTIN_SZWCSZ03 -1.8080822 0.0221358 -81.681 < 2e-16 ***
DESTIN_SZWDSZ01 0.8847786 0.0032457 272.598 < 2e-16 ***
DESTIN_SZWDSZ02 -1.0134375 0.0052518 -192.970 < 2e-16 ***
DESTIN_SZWDSZ03 0.5089895 0.0036337 140.077 < 2e-16 ***
DESTIN_SZWDSZ04 -0.5391818 0.0051060 -105.597 < 2e-16 ***
DESTIN_SZWDSZ05 -0.2960653 0.0047316 -62.572 < 2e-16 ***
DESTIN_SZWDSZ06 0.1082314 0.0038059 28.437 < 2e-16 ***
DESTIN_SZWDSZ07 -0.7178436 0.0057494 -124.855 < 2e-16 ***
DESTIN_SZWDSZ08 -0.1595135 0.0055042 -28.981 < 2e-16 ***
DESTIN_SZWDSZ09 -0.2931198 0.0042186 -69.483 < 2e-16 ***
DESTIN_SZYSSZ01 0.7706389 0.0034792 221.496 < 2e-16 ***
DESTIN_SZYSSZ02 -0.4208187 0.0046344 -90.804 < 2e-16 ***
DESTIN_SZYSSZ03 -1.1602553 0.0048797 -237.774 < 2e-16 ***
DESTIN_SZYSSZ04 -0.4453826 0.0044457 -100.182 < 2e-16 ***
DESTIN_SZYSSZ05 -1.8835365 0.0087245 -215.891 < 2e-16 ***
DESTIN_SZYSSZ06 -1.2555323 0.0067794 -185.197 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7349207 0.0092425 -79.515 < 2e-16 ***
DESTIN_SZYSSZ08 0.7160485 0.0034728 206.185 < 2e-16 ***
DESTIN_SZYSSZ09 -0.0362770 0.0036727 -9.877 < 2e-16 ***
log(dist) -0.9871576 0.0001519 -6497.379 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 100298738 on 21188 degrees of freedom
Residual deviance: 28758680 on 20570 degrees of freedom
AIC: 28893245
Number of Fisher Scoring iterations: 7I will check the R-square for this model as well.
# Compute R square of doubly constrained SIM
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)[1] 0.599689This seems to be an improvement over the previous models.
16.5 Model Comparison
A useful metric for comparing regression based models is Root Mean Squared Error. compare_performance() from performance package will be used to do compute this metric across the various models.
First, a list of models to be compared will be created.
# Create list of models
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Now, I can use proceed to use that list to generate metrics for the relevant models.
# Compare models
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-----------------------------------------
unconstrained | glm | 5059.346
originConstrained | glm | 4358.375
destinationConstrained | glm | 3930.670
doublyConstrained | glm | 3850.306Comparing across all models, it seems like doubly constrained model has the lowest RMSE of 3850.306.
16.6 Visualizing Fitted Values
To visualize the observed vs fitted values, I will need to extract the fitted values from each model and join it to the SIM_data dataframe. This will be done iteratively for each model.
Unconstrained SIM
# Extract fitted values
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)
# Join to SIM_data
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(uncTRIPS = "uncSIM$fitted.values")Origin Constrained SIM
# Extract fitted values
df <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)
# Join to SIM_data
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM$fitted.values")Destination Constained SIM
# Extract fitted values
df <- as.data.frame(decSIM$fitted.values) %>%
round(digits = 0)
# Join to SIM_data
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(decTRIPS = "decSIM$fitted.values")Doubly Constrained SIM
# Extract fitted values
df <- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)
# Join to SIM_data
SIM_data <- SIM_data %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM$fitted.values")Now, I can use ggplot to visualize for all 4 models at one with ggarrange() from ggpubr package
# Plot Unconstrained SIM
unc_p <- ggplot(data = SIM_data,
aes(x = uncTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
# Plot Origin Constrained SIM
orc_p <- ggplot(data = SIM_data,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
# Plot Destination Constrained SIM
dec_p <- ggplot(data = SIM_data,
aes(x = decTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
# Plot Doubly Constrained SIM
dbc_p <- ggplot(data = SIM_data,
aes(x = dbcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
# Visualize them together
ggarrange(unc_p, orc_p, dec_p, dbc_p,
ncol = 2,
nrow = 2)`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'